This section has just the one verse

Titus 2:6
Young men likewise exhort to be sober minded.

The phrase, "to be sober minded" is word G4993 and means "to be of sound mind, that is, sane, (figuratively) moderate: -- be in right mind, be sober (minded), soberly.

We will begin with the Barclay commentary.

THE CHRISTIAN CHARACTER
4. THE YOUNGER MEN
Titus 2:6

In the same way, urge on the younger men the duty of prudence.

THE duty of the younger men is summed up in one sentence – but it is a loaded one. They are told to remember the duty of prudence. As we have already seen, the man who is prudent has that quality of mind which keeps life safe and the security which comes from having all things under control.

The time of youth is necessarily a time of danger.

(1) In youth, the blood runs hotter and the passions speak more commandingly. The tide of life runs strongest in youth, and it sometimes threatens to sweep a young person away.

(2) In youth, there are more opportunities for going wrong. Young people are thrown into company where temptation can speak with a most compelling voice. Often, they have to study or to work away from home and from the influences which would keep them on the right path. The young man has not yet taken upon himself the responsibility of a home and a family; he has not yet made the kind of attachments to people and things that cannot be easily given up; and he does not yet possess the anchors which hold an older person in the right way through a sheer sense of obligation. In youth, there are far more opportunities to encounter disaster and to wreck one's life.

(3) In youth, there is often that confidence which comes from lack of experience. In almost every sphere of life, a younger man will be more reckless than his elders, for the simple reason that he has not yet discovered all the things which can go wrong. To take a simple example, he will often drive a car much faster simply because he has not yet discovered how easily an accident can take place or on how slender a piece of metal the safety of a car depends. He will often shoulder a responsibility in a much more carefree spirit than an older person, because he has not known the difficulties and has not experienced how easily disaster may happen. No one can buy experience; that is something for which only the years can pay. There is a risk, as there is a glory, in being young.

For that very reason, the first thing at which any young person must aim is self-control. We can never serve others until we have full control of self. ‘One who is slow to anger is better than the mighty, and one whose temper is controlled than one who captures a city’ (Proverbs 16:32).

Self-discipline is not among the more glamorous of the virtues, but it is the very stuff of life. When the eagerness of youth is supported by the solidity of self-control, something really great comes into life. ~Barclay Commentary

Now to the other commentaries beginning with the general and going to the specific.

First to the Matthew Henry Main. We will break into this long commentary that covers verses 1-10 and discuss what it has for verse 6.

4. Here is the duty of young men. They are apt to be eager and hot, thoughtless and precipitant; therefore they must be earnestly called upon and exhorted to be considerate, not rash; advisable and submissive, not willful and head-strong; humble and mild, not haughty and proud; for there are more young people ruined by pride than by any other sin. The young should be grave and solid in their deportment and manners, joining the seriousness of age with the liveliness and vigour of youth. This will make even those younger years to pass to good purpose, and yield matter of comfortable reflection when the evil days come; it will be preventive of much sin and sorrow, and lay the foundation for doing and enjoying much good. Such shall not mourn at the last, but have peace and comfort in death, and after it a glorious crown of life. ~Matthew Henry Main.

Now to the Matthew Henry Concise. This commentary covers verses 1-10.
 
 Old disciples of Christ must behave in everything agreeably to the Christian doctrine. That the aged men be sober; not thinking that the decays of nature will justify any excess; but seeking comfort from nearer communion with God, not from any undue indulgence. Faith works by, and must be seen in love, of God for himself, and of men for God's sake. Aged persons are apt to be peevish and fretful; therefore, need to be on their guard. Though there is not express Scripture for every word, or look, yet there are general rules, according to which all must be ordered. Young women must be sober and discreet; for many expose themselves to fatal temptations by what at first might be only want of discretion. The reason is added, that the word of God may not be blasphemed. Failures in duties greatly reproach Christianity. Young men are apt to be eager and thoughtless, therefore must be earnestly called upon to be sober-minded: there are more young people ruined by pride than by any other sin. Every godly man's endeavor must be to stop the mouths of adversaries. Let thine own conscience answer for thine uprightness. What a glory is it for a Christian, when that mouth which would fain open itself against him, cannot find any evil in him to speak of! ~Matthew Henry Concise.

Here are a couple of pieces from the Biblical Illustrator:

Young men likewise exhort to be sober minded
Sober mindedness
I. What it is.
1. You must be considerate and thoughtful, not rash and heedless. Take time to think; learn to think freely—to think for yourselves, of yourselves.

Note:  What this means, in spiritual terms, is that you do not allow others to think for you.  It means relying on God for the proven truth and constantly applying it to your life.

2. You must be cautious and prudent, not willful and heady. Fix rules of wisdom. Use reason and conscience. Be diffident of your own [Spirit-driven] judgment. Study Scripture.
3. You must be humble and modest, not proud and conceited. Be not above your business, above reproof, above religion.
4. You must be temperate and self-denying, not indulgent of your appetites.
5. You must be mild and gentle, not indulgent of your passions.
6. You must be chaste and reserved, not wanton or impure.
7. You must be staid and composed, not giddy and unsettled.
8. You must be content and easy, not ambitious and aspiring.
9. You must be grave and serious, not vain and frothy.

II. Considerations to enforce this exhortation.
1. You are reasonable creatures.
2. You are sinners before God.
3. You are setting out in a world of sorrows and snares.
4. Multitudes of the young are ruined for want of this sobriety of mind.
5. You are here upon trial for [the Kingdom].
6. You must shortly go to judgment.

III. Application:
1. Examine yourselves.

2. Exhort one another.

3. Contemplate the advantages of sober mindedness. You will
(1) Escape vanity of childhood and youth;
(2) Recommend yourselves to the favour of God and all wise men;
(3) Prepare for a useful and comfortable life, and a happy death [knowing you will be in the Kingdom of God].

4. Directions to make you sober minded.
(1) Espouse [adopt, embrace, invoke] sober principles.
(2) Meditate on serious things.
(3) Choose sober companions.
(4) Read sober books.
(5) Abound in sober work. ~Biblical Illustrator

Exhortation to sober mindedness
I. The necessity of this exhortation. This arises from
1. The ignorance and inexperience of youth.
2. Those constitutional inclinations which predominate in some more than in others.
3. The temptations by which youth is surrounded.
4. The vast importance of commencing well a course of life.

II. The character of that sober mindedness which the text recommends.
1. Its basis. Reverence for God, [repentance for sin], etc.
2. Its contrasts. Pride, rashness, obstinacy, petulance [bitter], sullenness [showing irritation and gloomy ill humor], presumption, etc.
3. Its objects. It should make you moderate in all things, etc.

III. The advantages which result from the possession and display of this sober mindedness.
1. It will qualify you for your relations to society.
2. It will greatly contribute to your usefulness wherever you are placed.
3. It will greatly increase your comfort. ~Biblical Illustrator

Discretion the safeguard of youth
This concise statement as to the exhortation to be addressed to young men may be regarded as a summary of all youthful virtues. The sins and follies of youth largely arise from want of thought. This fact, while it is no excuse for the sins committed, is an indication of the remedy to be sought. Let youths be trained to cultivate discretion, and, humanly speaking, they will be kept safe from the follies so common to their age. In a sermon to young men, discretion may be commended thus:

I. As the cultivation of the mental and moral powers with which God has endowed them.
II. As the fulfillment of the destiny which they are to fulfil in life.
III. As the fitting preparation for a higher life hereafter. ~Biblical Illustrator

Sober-minded youth
I. Some characteristics of this sober mind.
1. A habit of moral thoughtfulness.
2. Practical prudence and circumspection.
3. A modest and humble deportment.

II. Some particulars in which this grace of character should be displayed.
1. In all your plans and schemes for worldly happiness.
2. In all parts of your social intercourse—dress, discourse, Choice of recreations, etc.

III. A valuable agency by which this sober mindedness may be promoted. ~Biblical Illustrator

Now to the specific commentaries.

This verse is not broken out in any way.  It is one thought.

1] Young men likewise exhort to be sober minded.

Young men . . . be sober-minded. -  The precept, sober-minded, occurs four times in six verses, and may be accounted for by the volatile character of the Cretans. ~People's New Testament

Young men - exhort to be sober-minded - Reformation should begin with the old; they have the authority, and they should give the example. The young of both sexes must also give an account of themselves to God; sober-mindedness in young men is a rare qualification, and they who have it not plunge into excesses and irregularities which in general sap the foundation of their constitution, bring on premature old age, and not seldom lead to a fatal end. ~Adam Clarke

Young men likewise exhort to be sober minded. - Temperate, chaste, modest, moderate, wise, and prudent in all things: this is said to Titus, as being his province to instruct and exhort the young men; as it were proper and convenient for aged women to teach the young women how they should behave and conduct themselves. ~John Gill

Young men likewise exhort to be sober minded. -  A virtue rarely found in youth. ~John Wesley Explanatory Notes

Young men likewise exhort to be sober-minded - Margin, “discreet.” The idea is, that they should be entreated to be prudent, discreet, serious in their deportment; to get the mastery over their passions and appetites; to control the propensities [tendency] to which youth are subject; and that there should be such self-government, under the influence of, religion, as to avoid excess in everything. A well-governed mind, superior to the indulgence of those passions to which the young are prone, will express the meaning of the word here. They should be “steady in their behaviour, superior to sensual temptations, and constant in the exercise of every part of self-government.” Doddridge. The reasons for this are obvious:

(1) The hopes of the church depend much on them.
(2) a young man who cannot govern himself, gives little promise of being useful or happy.
(3) Indulgence in the propensities [natural inclination] to which young men are prone, will, sooner or later, bring ruin to the body and the soul.
(4) they are just at the period of life when they are exposed to special temptations, and when they need to exercise a special guardianship over their own conduct.
(5) like others, they may soon die; and they should be habitually in such a frame of mind, as to be prepared to stand before God. A young man who feels that he may be soon in the eternal world, cannot but be sensible of the propriety of having a serious mind, and of living and acting as in the immediate presence of his Maker and Judge. ~Barnes Notes

Let us look at some verses that speak to youth and related to our verse 6:

Ecclesiastes 11:9-10
9 Rejoice, O young man, in thy youth; and let thy heart cheer thee in the days of thy youth, and walk in the ways of thine heart, and in the sight of thine eyes: but know thou, that for all these things God will bring thee into judgment.
10 Therefore remove sorrow from thy heart, and put away evil from thy flesh: for childhood and youth are vanity.

Ecclesiastes 12:1
Remember now thy Creator in the days of thy youth, while the evil days come not, nor the years draw nigh, when thou shalt say, I have no pleasure in them;

1 Peter 5:5-10
5 Likewise, ye younger, submit yourselves unto the elder. Yea, all of you be subject one to another, and be clothed with humility: for God resisteth the proud, and giveth grace to the humble.
6 Humble yourselves therefore under the mighty hand of God, that he may exalt you in due time:
7 Casting all your care upon him; for he careth for you.
8 Be sober, be vigilant; because your adversary the devil, as a roaring lion, walketh about, seeking whom he may devour:
9 Whom resist stedfast in the faith, knowing that the same afflictions are accomplished in your brethren that are in the world.
10 But the God of all grace, who hath called us unto his eternal glory by Christ Jesus, after that ye have suffered a while, make you perfect, stablish, strengthen, settle you. [see sermon: Stablishment]

1 John 2:12-13
12 I write unto you, little children, because your sins are forgiven you for his name's sake.
13 I write unto you, fathers, because ye have known him that is from the beginning. I write unto you, young men, because ye have overcome the wicked one. I write unto you, little children, because ye have known the Father.

Let us finish with some quotes on the subjects of being moral, humble, sober minded, prudent [judicious in practical affairs], discreet, temperate, wise and master of passions [temptations].

Avoid Temptations: "It is easier to avoid temptation than to resist it."

Humbleness: “Selflessness. Humility. Truthfulness. These are the three marks of an honorable man.”

Humbleness: “Humility is the fundamental principle that builds up greatness. Arrogance on the other hand never brings anything good. When you are humble, you’ll learn to become better.”

Wisdom: "Affliction comes to us, not to make us sad but sober; not to make us sorry but wise."

Discreetness: "Heroes are never perfect, but they're brave, they're authentic, they're courageous, determined, discreet, and they've got grit."

Temperate: "The most temperate of persons is the one who controls himself, and in doubtful events is self-contained."

Wisdom: "A smart man makes a mistake, learns from it, and never makes that mistake again. But a wise man finds a smart man and learns from him how to avoid the mistake altogether."

Prudence: "Few things are brought to a successful issue by impetuous desire, but most by calm and prudent forethought."

Prudence: "Life has no blessing like a prudent friend."

Controlling Your Passions: "“Everybody in the world is seeking happiness—and there is one sure way to find it. That is by controlling your thoughts. Happiness doesn't depend on outward conditions. It depends on inner conditions.”

So, young men, be sober minded. This is the lesson of verse 6.