The initial pH is 7.64 and does not change, so the answer is 7.64
Water donating the same amount of OH- and H+ is not the correct reason. Water always donates the same amount of OH-/H+. If that was a reason for constant pH, you would not be able to change the pPh of any solution by adding water.
The trick here is that when you're adding water you're changing the concentrations of acid and conjugate by the same factor. That makes their ratio constant and gives you a constant [H]. That will be true even for solving different from water, which contributes only to [H].