Romans 4:6 Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works, 7 Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered. 8 Blessed is the man to whom the Lord will not impute sin.
Consider who David was in the scriptures. He was an adulterer and a murderer. Look at the turmoil his sin caused in his life. Even a man such as he could receive the righteousness of God. David is a picture of a sinner. He is a picture of all mankind, needing God to deal with our sin in forgiveness. Abraham and David together as described here by Paul represent God and how He justifies sinners. He both forgives sin because the debt is paid for those sins and imputes the righteousness earned by Christ Jesus to our accounts. That is justification in the eyes of God.
Romans 3:20 Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin.
Have you seen any work by the sinner, any condition that led to a just/right standing before God in our discussion. The answer is no and that is the point Paul is making. It is all of God in and by the Lord Jesus Christ. God would not impute sin to David as He was forbearing in waiting for the propitiation that would satisfy His holy judgment against the sins of His people. He was forbearing to all of us in the sacrifice that was Christ Jesus. God had purposed this in Christ and in due time came His cross. His cross paid for all the sin of all the elect for all of time all at one time. There was no forgiveness prior to the payment. Paul is continuing to point us to the substitutionary death of Jesus Christ. Instead of laying the sin of David to his own personal spiritual account, God would impute the sin of David to the account of Christ and take retribution upon the body and soul of Him in payment for his sins just that same as ours. Sin could not be sent away; there had to be recompense for our actions. God could not be just in letting sin slide. He has already pronounced the verdict.
Romans 6:23 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
Here we see both the verdict, death, and the solution, Jesus Christ. God would impute the works of our hands to Christ and in turn impute the works of Christ’s hands to us. That is our salvation.