Assume a reaction takes place in a basic solution to form the given products:

MnO4–(aq) + Cl–(aq) MnO2(s) + Cl2(g) (unbalanced)
Multiply to balance the charges in the reaction.

MnO4–(aq) + 8Cl–(aq) → MnO2(s) + 4Cl2(g)