To find the stronger base, find out which is the weaker acid. HI is the stronger acid thus weakest base.
F- is the answer.
Acidity and Size trend:
- (strongest bond, least acidic) HF < HCl < HBr < HI (most acidic, largest size)
- F- < Cl- < Br- < I- (most stable, largest size)
- strong bonds = weak acid