To balance
MnO4−+H2O2⟶MnO2+O2(1) Oxidation H2−1O2⟶0O2+2e−
Reduction +7MnO−4+3e−⟶+4MnO2
(2) Balancing the atoms & charge
H2O2+2OH−⟶O2+2e−
MnO−4+3e−⟶MnO2+4OH−
Balance O-atoms,
H2O2+2OH−⟶O2+2e−+2H2O⟶(1)
MnO−4+3e−+2H2O⟶MnO2+4OH−⟶(2)
(3) Electron gain equivalent to electron lost
(1)×3 & (2)×2
⇒3H2O2+6OH−⟶3O2+6e−+6H2O⟶(3)
2MnO4+6e−+4H2O⟶2MnO2+8OH−⟶(4)
Adding & simplifying (3) & (4) we get,
3H2O2+2MnO−4⇌2MnO2+3O2+2OH−+2H2O