It's a limiting reactant problem. Compare the moles of each reactant to the stoichiometric mix of NO2/H2O of 3/1:
108 g H2O (1 mole/18.02g H2O) = 5.99 moles water
186 L NO2 (1 mole/22.4 L @STP) = 8.30 moles NO2 (LR as you need 3x the water moles)
Now, just continue stoichiometric calculation using the LR:
8.30 moles NO2 (1 NO/3 NO2)( 30.01 g/mole NO) = g of NO
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