10 I- --> 5 I2 + 10 e-
16 H+ + 2 MnO4- + 10 e- --> 2 Mn2+ + 8 H2O
This yields the following final equation:
10 I- + 10 e- + 16 H+ + 2 MnO4- --> 5 I2 + 2 Mn2+ + 10 e- + 8 H2O
Get the overall equation by canceling out the electrons and H2O, H+, and OH- that may appear on both sides of the equation:
10 I- + 16 H+ + 2 MnO4- --> 5 I2 + 2 Mn2+ + 8 H2O

