I think the chemical reaction is:
N2H4 + 2 H2O2-> N2 + 4H2O
We are given the amount reactants allowed to react. This will be the starting point of the reaction. First, is to find the limiting reactant.
9.24 g H2O2 ( 1 mol / 34.02 g ) = 0.27 mol H2O2
6.56 g N2H4 ( 1mol / 32.06) = 0.20 mol N2H4
Since from the reaction we have 1:2 ratio of the reactants then the limiting reactant is hydrogen peroxide. We will use this to find the amount of N2 produced.
0.27 mol H2O2 ( 1 mol N2 / 2 mol H2O2 ) ( 14.01 g N2 / 1 mol N2) =1.89 g N2