First, let us consider the antecedents of the pronouns here. After all, you see here a repetition of the word “they,” and if you do not know what “they” are, then you are in danger of missing the point. Chasing antecedents is crucial.
In that pursuit, we have two helpers for this text. The first is sentence structure. Unless there is a compelling reason to look farther, we look for the closest nouns that match the pronoun logically. In this case, we should look back to Proverbs 6:20 where the father’s commandments and the mother’s teachings are commended. Here you have two things, which makes a “they,” and these fit logically with the ideas in 6:22.
There is another aid to the pursuit, though, and it is one you might not notice. If you have some of the more literal Bible translations, you will see a little footnote on the word “they” which marks that the word is more specifically “she.” She? Really? Yes, really. And then, if you have the ability through your brain or your computer to check the Hebrew, you will see this: commandments and teachings? Both are feminine nouns, so the proper pronoun in Hebrew is “she” rather than “they.” These are both also singular, though some English versions render them in plural for clarity.
So, what are “they?” The commandment of the father, the teaching of the mother. These are the two things that the young sons of Solomon need. To hold on tightly to what they have been taught and commanded.
It behooves parents to teach their children. Even if you are partnered with a school system to handle some of the teaching, you are still entrusted by God with that child to teach them, and help them grow. Solomon likely had wise men and tutors for his sons, but I see very little of Proverbs commanding his sons to follow the wise men. Instead, he counts the wise men as teaching what he would teach. This is a necessary unity, and should be mandatory for any partnership in teaching children.
Further, we ought to remember the value of what we have learned. I find it hard to improve on the clear statement here: value in guiding actions; value in protecting when we cannot; value in learning more as we go.
This is wisdom, and worth your time!