You'd neeed 35.3 mL.
Start by writing the balanced chemical equation for this neutralization reaction
The important thing to notice here is that you ahve a
This means that, in order to have a complete neutralization, you need equal numbers of moles of each compound.
SInce you know the molarity and volume of the potassium hydroxide solution, you can determine how many moles of
This means that you also had
Now simply use the hydroiodic acid solution's molarity to see what volume would contain this many moles
Expressed in mililiters, the answer will be