You have what's called a click clack waste, push it down it closes push it again it opens. Some of them just unscrew anticlockwise and clockwise to tighten. Some don't.
If it won't you need to unscrew the trap and check for a restriction that way, you will need to take the shelf out to loosen the trap. Just push up on the shelf on the left or right side and it should fall off the hangers.