Possible meanings are 1) David wrote the psalm or 2) the psalm is about David or 3) the psalm is in the style of David's psalms.
# when Nathan the prophet came to him
It can be stated clearly what Nathan did when he came to David, because this psalm is in response to that. AT: "when Nathan the prophet came to David and rebuked him" (See: [[rc://en/ta/man/translate/figs-explicit]])
# after he had slept with Bathsheba
"after David had slept with Bathsheba"
# because of your covenant faithfulness
The abstract noun "faithfulness" can be translated as an adjective. AT: "because you are faithful to your covenant" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])
# for the sake of the multitude of your merciful actions
Forgiving sins is spoken of as either 1) blotting them out or 2) erasing a written record of the sins. AT: "forgive my sins like someone wiping something away" or "forget my sins like someone who erases a record of sins" (See: [[rc://en/ta/man/translate/figs-metaphor]])
Being acceptable to God is spoken of as being clean. God makes people acceptable by forgiving their sins. AT: "Wash away all my sin" or "Forgive all my sins so that I will be acceptable to you" (See: [[rc://en/ta/man/translate/figs-metaphor]])
Being acceptable to God is spoken of as being clean. God makes people acceptable by forgiving their sins. AT: "Make me clean from my sin" or "forgive me for my sin so that I will be clean" (See: [[rc://en/ta/man/translate/figs-metaphor]])