$\begin{align}  & \text{Convert both sides to decimal system} \\ & \text{3}{{\text{2}}_{four}}={{22}_{x}} \\ & 3\times {{4}^{1}}+2\times {{4}^{0}}=2\times {{x}^{1}}+2\times {{x}^{0}} \\ & 12+2=2x+2 \\ & x=6 \\\end{align}$