What are the two possibilities for how old Adam and grace can reign in a person?
The old sin nature (old Adam) can reign like a king over a person, or the person can crucify it and let grace—God in Christ and the Holy Spirit—reign as king. Paul declares the old Adam shall not have dominion because believers are under grace, not law.
Les explains that in verse 14, old Adam and the old sin nature are interchangeable terms. The two possibilities are that old Adam will reign like a king, or we can crucify him and let grace—God in the person of Christ and the Holy Spirit—reign as king. Paul comes back and says the old Adam shall not have dominion over you because you are not under law but under grace. Les qualifies that not being under law does not mean casting aside the Ten Commandments; they are still holy, perfect, the mind of God, and the criteria for social behavior for both Christian and non-Christian. They are not a criteria of doctrine, which is why Les has no compunction about having them in public schools, as they are simply the mind of God for mankind's own good.