Given,
Maximum compression$\left(A\right)=2x_0$

Distance of block from wall$\left(x\right)=x_0$

Mass of block$=m \mathrm{kg}$

Since initially block is at extreme position, its equation will be-

$x=A\sin \left(\omega t+\frac{\mathrm{\pi }}{2}\right)=2x_0 \cos \omega t$

When block hit the wall, its position will be $x=-x_0$

Put this value in equation of $\mathrm{SHM}$-

$-x_0=2x_0 \cos \omega t$

$\Rightarrow \cos \left(\omega t\right)=-\frac{1}{2}=\cos \frac{2\mathrm{\pi }}{3}$
$\Rightarrow \omega t=\frac{2\mathrm{\pi }}{3}$

For given $\mathrm{SHM}$-

$\Rightarrow \omega =\sqrt{\frac{k}{m}}$

$\therefore t=\frac{2\mathrm{\pi }}{3}\sqrt{\frac{m}{k}}$