(a) Skeletal ionic equation :
MnO-4 + Br- ⟶ MnO2 + BrO-3
Assigning oxidation numbers:

Calculates the increase and decrease in oxidation number and make them equal:

Balancing ionic changes:
2MnO-4 + Br- ⟶ 2MnO2 + BrO3- + 2OH-
Balancing H and O atoms:
2MnO-4 + Br- + H2O ⟶ 2MnO2 + BrO3- + 2OH-
(b) Oxidising agent - MnO-4
Reducing agent - Br