"I will no longer remember their sins and lawlessness.'" or "I will no longer think about their sins and lawlessness.'" This is the second part of the Holy Spirit's testimony ([Hebrews 10:15-16](./15.md)). You can make this explicit in the translation by ending the quotation at the end of verse 16 and starting a new quotation here. Alternate translation: "Then next he said, 'Their sins and lawlessness I will remember no longer.'" (See: [[rc://en/ta/man/jit/figs-explicit]])
The words "sins" and "lawlessness" mean basically the same thing. Together they emphasize how bad the sin is. Alternate translation: "The things they did that were forbidden and how they broke the law" (See: [[rc://en/ta/man/jit/figs-doublet]])