"Peut-il avoir le livre ?"
The most basic way to learn this rule is when you have more than one verb in sentence, you only conjugate one of them. You never conjugate two in a row when there's only one subject in the sentence. You conjugate "pouvoir" for "il" and you use the unconjugated form or infinitive of "have", which is "avoir". Think of English, when we say "I want to have", the "to have" part is the infinitive. In French this would be "je veux avoir", not "je veux ai". Hope that helps!
I like to think of "pouvoir" in this sense as "is able". Then the infinitive verb that follows makes sense from an English translation point of view. So in my head I would think of this as "He is_able to_have the book. If you think of "pouvoir" simply as "can" it's more confusing as then you get "He can to_have the book.