I need to put a 4 inch hole in a 16 inch ceramic tile.
There are special bits for this. And you'll need a darned heavy duty drill. Your local hardware store can show you the right stuff.
Drill a small hole, say 1/4 then useing a tile saw cut the large hole. Tile saws are availlable fro any DIY stor.
Drill many small holes in a circular pattern. Remember on the cartoons where a person uses a machine gun to cut a door in a wall? You can do the same with a small ceramic drill bit. Use a dremel tool to 'file' the edges smooth