God spoke the Ten Commandments to Israel, beginning with His deliverance from Egypt and commanding exclusive worship, reverence for His name, Sabbath rest, honor for parents, and justice toward neighbors (Exodus 20:1-21).
1And God spoke all these words: 2“I am the LORD your God, who brought you out of the land of Egypt, out of the house of slavery. 3You shall have no other gods before Me.
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.