Fe(OH)_3(s) $\rightleftharpoons$ Fe³⁺_(aq) + 3OH^$-$_(aq)

Equilibrium constant, K_c = ${{\left[ {F{e^{3 + }}} \right]{{\left[ {O{H^ - }} \right]}^3}} \over {\left[ {Fe{{\left( {OH} \right)}_3}} \right]}}$

We know, equilibrium constant remains same at constant temperature.

Now, let the increase in concentration of Fe³⁺ be x times.

$\therefore$ K_c = ${{\left[ {x \times F{e^{3 + }}} \right]{{\left[ {{1 \over 4} \times O{H^ - }} \right]}^3}} \over {\left[ {Fe{{\left( {OH} \right)}_3}} \right]}}$

= ${x \over {64}}{{\left[ {F{e^{3 + }}} \right]{{\left[ {O{H^ - }} \right]}^3}} \over {\left[ {Fe{{\left( {OH} \right)}_3}} \right]}}$

$\Rightarrow$ K_c = ${x \over {64}}$K_c

$\Rightarrow$ ${x \over {64}}$ = 1

$\Rightarrow$ x = 64