The picture is of the sinner offering the "parts of his body" to his master or king. One's "body parts" are a synecdoche for the whole person. AT: "Do not offer yourselves to sin so that you do what is not right" (See: [[rc://en/ta/man/translate/figs-synecdoche]])
Here "now living" refers to the believer's new spiritual life. AT: "But offer yourselves to God, because he has given you new spiritual life" (See: [[rc://en/ta/man/translate/figs-explicit]])
Here "parts of your body" is a synecdoche that refers to the whole person. AT: "let God use you for what is pleasing to him" (See: [[rc://en/ta/man/translate/figs-synecdoche]])
Paul speaks of "sin" here as if it were a king who rules over people. AT: "Do not let sinful desires control what you do" or "Do not allow yourselves to do the sinful things you want to do" (See: [[rc://en/ta/man/translate/figs-personification]])
To be "under law" means to be subject to its limitations and weaknesses. You can make the full meaning explicit in your translation. AT: "For you are no longer bound to the law of Moses, which could not give you the power to stop sinning" (See: [[rc://en/ta/man/translate/figs-explicit]])
To be "under grace" means that God's free gift provides the power to keep from sinning. You can make the full meaning explicit in your translation. AT: "but you are bound to God's grace, which does give you the power to stop sinning" (See: [[rc://en/ta/man/translate/figs-explicit]])