The hydrolysis constant for ${\mathrm{ZnCl}}_2$ will be

${\mathrm{Zn}}^{++} + 2{\mathrm{H}}_2\mathrm{O} \rightleftharpoons \mathrm{Zn}{\left(\mathrm{OH}\right)}_2 + 2{\mathrm{H}}^{+}$

$\therefore {\mathrm{K}}_{\mathrm{h} }= \frac{\left[\mathrm{Zn}{\left(\mathrm{OH}\right)}_2\right] {\left[{\mathrm{H}}^{+}\right]}^2}{\left[{\mathrm{Zn}}^{++}\right]}$             …. (1)

$\mathrm{Zn}{\left(\mathrm{OH}\right)}_2 \rightleftharpoons {\mathrm{Zn}}^{++} + 2{\mathrm{OH}}^{-}$

$\therefore {\mathrm{K}}_{\mathrm{b} }= \frac{\left[{\mathrm{Zn}}^{++}\right] {\left[{\mathrm{OH}}^{-}\right]}^2}{\left[\mathrm{Zn}{\left(\mathrm{OH}\right)}_2\right]}, {\mathrm{K}}_{\mathrm{w} }= \left[{\mathrm{H}}^{+}\right] \left[{\mathrm{OH}}^{-}\right]$

$\therefore \frac{{\mathrm{K}}_{\mathrm{w}}^2}{{\mathrm{K}}_{\mathrm{b}}} = {\mathrm{K}}_{\mathrm{h}}$