In this question, we have to find 3 types of reactions, the reduction half-reaction, which is the reaction that will show only the element or compound that was reduced (gained electrons), the oxidation half-reaction, the element or compound was oxidized (lost electrons), and finally, the overall reaction, which will show both reduction and oxidation in one place:
Oxidation half-reaction
Cl^- -> Cl2
Reduction half-reaction
MnO4^- -> Mn^2+
Overall reaction:
MnO4^- + Cl^- -> Mn^2+ + Cl2