How to apply the Henderson–Hasselbalch equation when adding KOH to an acidic acid buffer?
If the initial solution is just acetic acid and water, and the pH is 3.97, this means that it is a very dilute solution, less than 0.001M acetic acid. See http://depts.washington.edu/chem/facilserv/lecturedemo/pHofAceticAcid-UWDept.ofChemistry.html

and Does the number of H+ ions in solution go up on dilution of a weak acid?

Therefore, of the 0.025 moles of OH-, almost all (more than .024 moles) will remain unreacted.  

pH = 14 - pOH

pH = 14 + log(0.025) = 12.4

In a different situation, where you added less strong base than weak acid, the Henderson-Hasselbach equation would be helpful, but it is not helpful in this example.