Mn is for manganese I think. Ok first of all check the number of molecules on each side. on the left, Mn has 1, Oxygen has 2, Nitrogen has 1, Hydrogen has 4. On the right hand, Mn has 2,Oxygen has 3, nitrogen has 1 and Hydrogen has 5. all need to be balanced.
So the resulting coefficients on both sides should be;
2(MnO2) + 2(NH4) --- > Mn2O3 + 2(NH3) + H2O
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