This is a simple puzzle of guessing the correct door in each room, but because this game is very easy and forgiving so even if you choose the wrong door in any room or get caught by the moving maids you will only be forced back to this room.
To find the correct doors without guessing, you need to get the ghost in the art room to help you
and you also need to fix the eye of truth by going to the room that was previously locked by door 9 in the same art room. (I don't remember if you actually need to do this part or not)