Why does Peter ask for Claire's birth date in reverse order?

If the ID is fake, Claire has most likely memorized the date on the ID in normal month$/$day$/$year order; so$,$ asking for the year first breaks that order, breaks the memory.

He has already determined her ID is fake because of her appearance; so$,$ he is just having a bit of fun at her expense.

After proving the ID is fake, he must distract Claire so he can slip the ID into his pocket without her noticing. Giving her a question she is not ready for creates that distraction.

He is required to expose Claire's deception first, which he does by observation, but he is also required to prove that he knows she is underage, which he does by the year.