4 KOH + 2 Br20 KBrIIIO2 + 3 KBr-I + 2 H2O

This is an oxidation-reduction (redox) reaction:

3 Br0 + 3 e- 3 Br-I (reduction)

Br0 - 3 e- BrIII (oxidation)

Br2 is both an oxidizing and a reducing agent (disproportionation).