Answer
Please see the work below.
Work Step by Step
We know that if the reaction is asked then
$K_c=\frac{[NH_3]^2[O_2]^{\frac{5}{2}}}{[NO]^2[H_2O]^3}$
and if the reaction is reversed then
$K_c=\frac{[NO]^2[H_2O]}{[NH_3]^2[O_2]^{\frac{5}{2}}}$