Romans 4:3 the story we’re given is a God-story, not an Abraham-story. What we read in Scripture is, “Abraham entered into what God was doing for him, and that was the turning point. He trusted God to set him right instead of trying to be right on his own.” (The Message Bible)
This is the Message Bible rendition of “Abraham believed God and it was credited to him as righteousness.” “Believe” becomes “trusted” and “righteousness” becomes “set him right.” Faith (belief) and righteousness are tough concepts. I think faith has to do with being convinced something is true even when you might still be dealing with some doubt. It also means being willing to say it out loud to others and having it determine your actions. Righteousness is being in the right with God, doing the right thing, being the right kind of person. Paul in this passage is saying that God did this for Abraham and, a few verses later, says God does this for us. How do you experience faith? What is your idea of righteousness? How do you get right with God?