A game of peak-a-boo with his dad excites William during the first six months of his life because William actually thinks his dad has disappeared. This is because William lacks:

Answer: Object permanence

Explanation: Object permanence refers to the mental ability of a child to know or belief that an object continue to exist even when they can no longer be heard, seen or felt. At the very early stage of a child, they seem to belief that once an object can no longer be heard or seen, then such objects has seized to exist. Such that when an object is hidden from a child view or taken out of sight, they belief such object has disappeared because they lack the mental ability to realize that maybe the object was hidden or kept away from them.