1. Write the relevant half-reaction for permanganate in acidic medium

In acidic medium, permanganate is reduced as:

This shows that 1 mole of $\mathrm{MnO_4^-}$ requires 8 moles of $\mathrm{H^+}$ for its reduction.

2. Write the oxidation half-reaction for oxalate ion

Oxalate ion is oxidised to carbon dioxide as:

3. Balance electrons

To match electrons, multiply the oxalate half-reaction by 5 and the permanganate half-reaction by 2 if writing the full reaction. But the question asks only for the number of moles of $\mathrm{H^+}$ required by 1 mole of $\mathrm{MnO_4^-}$.

From the permanganate half-reaction directly:

4. Check with full balanced reaction

The full balanced reaction in acidic medium is:

So, per mole of $\mathrm{MnO_4^-}$:

Thus, the number of moles of $\mathrm{H^+}$ required is 8.