Br- + MnO2 → Br2 + Mn2+ ?
In order to balance this equation, we have to have the same number of atoms of each element of both sides. This is how to do this:
2Br− + MnO2 →Br2 + Mn + O2
Br is oxidized, because it loses electrons. Mn and O are reduced, because they gain electrons. Oxidizing agents are Mn and O, because they are reduced. And reducing agent is Br, because it is oxidized.