The balanced chemical reaction is:
4NH3 + 6NO → 5N2 + 6H2O
We are given the amount of nitric oxide to be used in the reaction. This will be the starting point of the calculations.
27.8 g NO ( 1 mol NO / 30.01 g NO ) ( 4 mol NH3 / 6 mol NO ) ( 17.0337 g NH3 / 1 mol NH3 ) = 10.52 g NH3