The Y-hook is the small metal hook that provides the connection from the beaded chain to the flush lever. The flush lever is attached to the toilet handle, and lifts when the handle is pressed. This action pulls the chain to lift the flapper and allows water to travel from the tank down into the bowl. The design of a Y-hook often allows it better stability in securing the chain to the flush lever.

...
A toilet with a faulty Y-hook will not flush.

Step 1

Turn the toilet's shut-off valve all the way to the right. This shuts off water from entering the tank as you work. Remove the tank lid. Flush the toilet and continue pressing down the handle to allow as much water as possible to drain from the tank.

Step 2

Detach the chain from the flush lever inside the tank and remove the present hook on the end of the chain, if there is one. Insert the Y-hook into a link of the chain. Squeeze the sides of the Y hook together and insert it through a hole in the flush lever and release the Y hook. Examine whether the chain is tight enough to prevent it from slipping underneath the flapper after the flapper rises, but not so tight that it holds the flapper up from its seat when the toilet is not in use.

Step 3

Squeeze the sides of the Y-hook together and push it out of the flush lever hole, if the chain is too long. Remove the Y-hook from the chain and slip into a lower link of the chain. Reinstall the Y-hook into a hole on the flush lever. Experiment and place it in a different flush lever hole, if necessary, to create the right amount of slack in the chain.

Step 4

Cut off any extra chain, using a pair of snips, but don't make the chain too short. Turn the shut-off valve counterclockwise and allow the tank to refill with water. Flush the toilet and make certain the flapper rises and seats properly, without interference from the chain. Place the lid on the tank.