$W_{2 F}=2 F x_{2 C}$
$0-\frac{1}{2} k x_{\mathrm{max}}^{2}+F X_{1 C}+2 F x_{2 C}=0.......ii$
$\frac{1}{2} k_{\max }^{2}=F x_{1 C}+2 F x_{2 C}$
$x_{\max }=x_{1 C}+x_{2 C}$
From the concept of centre of mass
$M x_{1 C}=2 M x_{2 C}$
$X_{1 C}=2 x_{2 C}$
$\therefore x_{1 C}+2 X_{2 C}=x_{\max }$
$\therefore 3 x_{2 C}=x_{\max }$
$x_{2 C}=\frac{x_{\max }}{3}$ and $x_{1 C}=\frac{2 x_{\max }}{3}$ Puttng the values in eqn ii
$\frac{1}{2} k x_{\max }^{2}=F\left(\frac{2 x_{\max }}{3}\right)+2 F\left(\frac{x_{\max }}{3}\right)$
$\frac{1}{2} k x_{\max }=\frac{2 F}{3}+\frac{2 F}{3}$
$x_{\max }=\frac{8 F}{3 K}$
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