8 NaOH + Mn + 6 KMnO4 → 4 Na2MnO4 + 3 K2MnO4 + 4 H2O
This is an oxidation-reduction (redox) reaction:
Mn0 - 6 e- → MnVI (oxidation)
6 MnVII + 6 e- → 6 MnVI (reduction)
Mn is a reducing agent, KMnO4 is an oxidizing agent (synproportionation (comproportionation)).