General procedure:
1. write oxidation and reduction as separate equations
2. balance everything OTHER THAN O and H
3. balance O and H by adding H2O and H+
4. balance charge (this is the final step for rxn in acidic sln.)
5. multiply each reaction with least common factor of # of electrons to cancel e- on overall rxn.
6. if rxn happens in basic sln, add OH- to the side that has H+, and combine OH- with H+ to form H2O
This question is in acidic condition according to your answer, therefore:
oxidation: (2Br- --> Br2 + 2e-) * 5
reduction: (MnO4- + 8H+ + 5e- --> Mn2+ + 4H2O) * 2
overall rxn (add everthing up from the top two equations): 16H++2MnO4-+10Br--->5Br2+2Mn2++8H2O