Assuming the first term in your equation is a typo for permanganate (MnO4-)
Your half reactions are:
MnO4- -> MnO2
AsO3^-3 -> AsO4^-3
Add water to balance out O's, then H+ to balance out H's, then electrons to balance out total charges.
MnO4- + 4H+ + 3e- -> MnO2 + 2H2O
AsO3^-3 + H2O -> AsO4-3 + 2H+ + 2e-
2(MnO4- + 4H+ + 3e- -> MnO2 + 2H2O)
3(AsO3^-3 + H2O -> AsO4-3 + 2H+ + 2e-)
When you balance out the electrons by multiplying coefficients, you can see that AsO4^-3 will have a coefficient of 3 for the remainder of the balancing steps, and that will be your answer.
2MnO4- + 8H+ + 6e- -> 2MnO2 + 4H2O
3AsO3^-3 + 3H2O -> 3AsO4-3 + 6H+ + 6e-
2MnO4 + 3AsO3^-3 + 2H+ -> 2MnO2 + 3AsO4^-3 + H2O
Since it's in basic conditions we have to add -OH to eliminate the H+, forming water
2MnO4 + 3AsO3^-3 + 2H+ + 2-OH -> 2MnO2 + 3AsO4^-3 + H2O + 2-OH
2MnO4 + 3AsO3^-3 + 2H2O -> 2MnO2 + 3AsO4^-3 + H2O + 2-OH
2MnO4 + 3AsO3^-3 + H2O -> 2MnO2 + 3AsO4^-3 + 2-OH
If MnO^4- was in fact not a typo, then 😕