

In acidic medium,
ClO2 + e- → ClO2-
And then,
H2O2 → O2 + 2H+ + 2e-
Now multiply the first one by 2 to get the same number of electrons on both sides:
2ClO2 + 2e- → 2ClO2-
Adding the equations and eliminate the electrons:
H2O2 + 2ClO2 → 2ClO2- + O2 + 2H+
This is now balanced. The charges are the same on both sides and the number of atoms of each element is the same on both sides.
The oxidising agent is the one which gains electrons and is itself reduced.
