As far as the east is from the west, so far has he removed our transgressions from us.
David chooses his directions carefully. North and south have poles, and if you travel far enough you will reach them. East and west do not. You can walk east for the rest of your life and never arrive at a place where east becomes west.
That is the distance God has put between you and your sin. Not far. Unreachable.
Notice too that David writes in the past tense. He does not say God will remove our transgressions once we improve, or that the matter is still under consideration. He says it has already been done.
And the closing words matter as much as the opening ones: from us. The removal is not merely an entry changed in a ledger. It is a separation between you and the thing you are most ashamed of, and it has already happened. If you are still carrying it, you are carrying something that is no longer there.