(N/A) The equilibrium constant expression $K_{C}$ is defined as the ratio of the product of concentrations of products raised to their stoichiometric coefficients to the product of concentrations of reactants raised to their stoichiometric coefficients.
Given $K_{C} = \frac{[NH_{3}]^{4}[O_{2}]^{5}}{[NO]^{4}[H_{2}O]^{6}}$,the species in the numerator ($NH_{3}$ and $O_{2}$) are the products,and the species in the denominator ($NO$ and $H_{2}O$) are the reactants.
The stoichiometric coefficients correspond to the powers in the expression.
Thus,the balanced chemical equation is:
$4NO_{(g)} + 6H_{2}O_{(g)} \leftrightarrow 4NH_{3_{(g)}} + 5O_{2_{(g)}}$