4 H2O (l) + 2 KMnO4 (aq) + 6 NaBr (aq) → 6 NaOH (aq) + 2 KOH (aq) + 2 MnO2 (s) + 3 Br2 (aq)
This is an oxidation-reduction (redox) reaction:
6 Br-I - 6 e- → 6 Br0 (oxidation)
2 MnVII + 6 e- → 2 MnIV (reduction)
NaBr is a reducing agent, KMnO4 is an oxidizing agent.