Assume a reaction takes place in a basic solution to form the given products: mno4-(aq) + cl-(aq) > mno2(s) + cl2(g) (unbalanced)
i. balance the given half reactions for atoms and charge

To balance, we write it in its half reactions and balance the half reactions by adding H2O, OH-, H+ and electrons. We do as follows:

MnO4-(aq) + Cl-(aq) > MnO2(s) + Cl2(g) 

2 (2H2O + MnO2 --> MnO4- + 4H+ 3e- )
3 (2e- + Cl2 --> 2Cl- )

4H2O + 2MnO2 > 2MnO4- + 8H+ + 6e- 
6e- + 3Cl2 > 6Cl- 

4H2O + 2MnO2 + 3Cl2 > 2MnO4- + 6Cl- + 8H+ 

Since it is in a basic solution,

8OH- + 2MnO2 + 3Cl2 > 2MnO4- + 6Cl- + 4H2O