Agame of peek-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:

object permanence

Explanation:

William still hasn’t developed what Piaget defined as object permanence. Object permanence is the ability children have to understand that an object exists even if they cannot see it. Baby William is only six months old, and he hasn’t developed that ability yet. That's why he believes his dad disappears when he doesn't see him. He still cannot make mental representation of objects and lacks symbolic thought. Object permanence usually develops when the child is between 18 and 24 months old.

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