What type of energy does a ball on top of a hill or a child on top of a slide have?

The answer they want you to give is "potential energy". This is in fact a nonsense concept designed by school teachers to make their equations add up. If a mole dug a huge hole under the slide, the kid would suddenly have a load more "energy" but if a dwarf filled the hole up again and made a mound of earth up to the top of the kid's head, all his "energy" would have disappeared.