Ionisation of $N{H}_{4}OH$ is supressed by the addition of $N{H}_{4}Cl$, because-

$N{H}_{4}OH$ is a weak electrolyte but $N{H}_{4}Cl$ is a strong electrolyte

$N{H}_{4}OH\rightleftharpoons N{H}_4^{+}+O{H}^{-}$

$N{H}_{4}Cl\to N{H}_4^{+}+C{l}^{-}$

Due to the common ion effect of  $N{H}_4^{+}$ the ionization is suppressed.

Hence  the right answer is (C)  common ion effect of $N{H}_4^{+}$ ion