2 KMnO4 (aq) + H2O2 (aq) → 2 MnO2 (s) + 2 O2 (g) + 2 KOH (aq)
This is an oxidation-reduction (redox) reaction:
2 MnVII + 6 e- → 2 MnIV (reduction)
2 O-I - 2 e- → 2 O0 (oxidation)
2 O-II - 4 e- → 2 O0 (oxidation)
KMnO4 is an oxidizing agent, H2O2 is a reducing agent, KMnO4 is a reducing agent.
This is a precipitation reaction: MnO2 is the formed precipitate.
This is a gas evolution reaction, O2 is the formed gas.