This is how I would do it
2I- ---->I2 + 2e-
8H+ + 5e- + MnO4- --->Mn2+ + 4H20 (you get 8H+ by finding the balancing the equation)
Now, you need to get equal number of electrons on each side
so,
(2I- ---->I2 + 2e-)*5
(8H+ + 5e- + MnO4- --->Mn2+ + 4H20)*2
Now, we get:
16H+ + 10e- + 2MnO4- + 10I- -----> 5I2 + 10e- + 2Mn2+ + 4H20
electrons cancel out
So you are left with:
16H+ + 2MnO4- + 10I- -----> 5I2 + 2Mn2+ 4H20
So, sum of co-efficent should be : 16+2+10+5+2+4 = 42
*Plz correct me if I am wrong (I am not sure if you are suppose to include H20 and H+ in the sum)