The parents wouldn’t claim on their tax return that they paid $4k towards tuition. This would have to be done with their child (the student) claiming on his/her tax return that $14k and not $10k of the scholarship is taxable, thus freeing up $4k of the scholarship money spent on tuition to be used as a qualified expense for the parents to claim the AOTC. This assumes that the child is a tax dependent on the parents’ return.