How do we apply this verse in Proverbs 27:11?

Jehovah permitted Satan to test the integrity of God's loyal servant Job. As a result, Job lost his livestock, his children, and his health. But when Satan challenged Job's integrity, he had more in mind than just the man Job. "Skin in behalf of skin, and everything a man has he will give in behalf of his soul," claimed Satan. Satan was claiming that a man can be bought. That challenge raised an issue that went far beyond Job as an individual and has continued long after Job's death. Job 2:4.

It was 600 years after Job's trials that the words of Proverbs 27:11 were written by Solomon, who was inspired by God to write them. So Satan was still challenging Jehovah implying that a man could be persuaded to break his integrity if put under enough pressure.

In a vision given to the Apostle John, Satan was seen accusing God's servants following his eviction from the heavenly realm some time after the establishment of God's Kingdom in heaven in 1914.

There are three important lessons to be learnt from the book of Job which have a direct bearing on Proverbs 27:11. First, the trials of Job expose the real enemy of mankind and the source of opposition against God's people. That enemy is Satan.

Second, no matter what trials we may encounter, having a close relationship with God will enable us to maintain our integrity just like it helped Job.

And thirdly, when trials occur and we are tested in some way, God supports us just as he did Job. By maintaining a course of integrity, we give a reply to Satan and prove him to be the liar that he is. And we make Jehovah's heart glad by giving Satan the answer he doesn't want.

When we make wise decisions based on the principles set out in the Bible we bring joy to our God Jehovah.He cares about us and wants us to benefit ourselves following his guidance-Isaiah 48:17,18.Learn more about Jehovah by visiting the jw.org website.

God’s heart can be made glad by his servants because of their faithfulness and loyalty to him. Satan the Devil has constantly challenged the rightfulness of God’s sovereignty and the integrity of all those serving God. Job 1:9-11 

To them apply the words: “Be wise, my son, and make my heart rejoice, that I may make a reply to him that is taunting me.” Prov 27:11 God’s people in the earth can cause God to rejoice by faithfulness and loyalty to him.  Isa 65:19

Now consider this question: What kind of gift can you offer your Creator, Almighty God? At first, the very idea might sound absurd.

 What does the Almighty need from a mere human? What could you possibly give him that he does not already possess? 

The Bible answers at Proverbs 27:11: “Be wise, my son, and make my heart rejoice, that I may make a reply to him that is taunting me.”

Just do the best we can so our parents can be proud of us.

Many of God’s servants are in situations that involve personal suffering. Their suffering continues because God has not yet destroyed the wicked and brought about the foretold restoration of mankind. Should this embitter us? Or can we see such situations as opportunities to have a share in proving the Devil a liar? We can be strengthened to do so if we keep in mind the appeal: “Be wise, my son, and make my heart rejoice, that I may make a reply to him that is taunting me.” (Proverbs 27:11) Satan, the one who taunts Jehovah, charged that if people suffer material loss or physical affliction, they will blame God, even curse him. (Job 1:9-11; 2:4, 5) We bring joy to Jehovah’s heart when, by our loyalty to him in the face of hardships, we show that such is not true in our case.

The speaker is the youth's father, his teacher, or some friend. The reproach (2nd line) probably refers to some real or contemplated misdemeanor by the youth. "The speaker is concerned for the youth's career, and desires that he may so conduct himself as to furnish a triumphant answer to all assailants."

https://www.studylight.org/commentaries/eng/bcc/pr...

11 Be wise, my son, and bring joy to my heart;

    then I can answer anyone who treats me with contempt.

11 My son, be wise, and make my heart glad, that I may answer him that reproacheth me.

It seems to me that it's talking about being secure with love for a son, which causes a person to deal with adversity with the same kind of love.

And just another thing where your Sky Daddy's testing you see what you're going to do about it. Hey what do you think about this I might have 48 meanings but if you get the right one in the sky Daddy love you

By being wise

Proverbs 27:11 — Be wise, my child, and make my heart glad. Then I will be able to answer my critics.

We apply it by being on the right side of the current universal issue.  God is still being taunted just as he was in the case of Job.  Keep our integrity just as Job did.  The universal issue is still being tried in the greatest court of law.