What does Psalm 51:6 mean?

David acknowledges in this verse that God takes pleasure in truth in a person's heart and soul, but David's heart and soul were defiled by sin. He had deceived himself by thinking he could get away with his sins. He covered them up, but God exposed them, and now David longed for truth and wisdom.

The Bible warns, "Be sure your sin will find you out" (Numbers 32:23). Achan lived during Israel's conquest of Canaan, but like David, he sinned against God and then tried to cover it up. God had commanded His people to keep themselves from everything in Jericho that was devoted to destruction and to commit all the silver and gold, and every bronze and iron vessel, to the Lord's treasury (Joshua 6:17–19). However, Achan sinned by taking a beautiful cloak, 200 shekels of silver, a bar of gold weighing 50 shekels and burying them in his tent (Joshua 7:20–21). His coverup did not succeed. When his sin was exposed, he was stoned to death (Joshua 7:25). The Lord values truth but abhors deceit (Proverbs 6:16–19).