It is said on the daily quest to complete 3 puzzle, I had completed 2 new puzzle and 4 old ones and the mision do not complete or mark any as puzzle as done.
Wait, what do you mean with “4 old ones”?
Because puzzles from your replay mode and the ones completed before you got the quest won’t count towards this daily. Don’t worry though, you won’t get this quest again later on; those are specific single player content dailies, only showing up a single time each.