2 KMnO4 + 2 H2O2 → 2 O2 + 2 H2O + K2MnO4 + MnO2
This is an oxidation-reduction (redox) reaction:
MnVII + e- → MnVI (reduction)
MnVII + 3 e- → MnIV (reduction)
4 O-I - 4 e- → 4 O0 (oxidation)
KMnO4 is an oxidizing agent, KMnO4 is an oxidizing agent, H2O2 is a reducing agent.