Moses restated the Ten Commandments to the generation entering Canaan and recalled how Israel asked him to mediate after hearing God's voice from the fire. He called them to walk in all the way the LORD commanded (Deuteronomy 4:44-5:33).
44This is the law that Moses set before the Israelites.
Paul quotes the command, "Do not covet." He uses it to show how the law made him aware of sin.
What then shall we say? Is the law sin? Certainly not! Indeed, I would not have been mindful of sin if not for the law. For I would not have been aware of coveting if the law had not said, “Do not covet.”
Exodus 20:17 and Deuteronomy 5:21 both forbid coveting. Romans 7:7 repeats the command. Paul says the law taught him what coveting was.
Paul quotes four commands from the Ten Commandments. He says they are summed up in the command, "Love your neighbor as yourself."
Be indebted to no one, except to one another in love. For he who loves his neighbor has fulfilled the law. The commandments “Do not commit adultery,” “Do not murder,” “Do not steal,” “Do not covet,” and any other commandments, are summed up in this one decree: “Love your neighbor as yourself.” Love does no wrong to its neighbor. Therefore love is the fulfillment of the law.
Exodus 20:13-17 and Deuteronomy 5:17-21 contain the commands against adultery, murder, theft, and coveting. Leviticus 19:18 commands love for one's neighbor. Romans 13:8-10 quotes these commands and says that love does no wrong to a neighbor.