H2O + 2 KMnVIIO4 + 3 NaNIIIO2 2 KOH + 2 MnIVO2 + 3 NaNVO3

This is an oxidation-reduction (redox) reaction:

2 MnVII + 6 e- 2 MnIV (reduction)

3 NIII - 6 e- 3 NV (oxidation)

Change the oxidation states