Answer
The distance the spring can be stretched without the box moving when it is released is $9.8cm$
Work Step by Step
The box will start moving when the restoring force $F_x$ overcomes $f_s^{max}$, so when $$F_x=f_s^{max}$$ $$kx=\mu_sF_N=\mu_smg$$ $$x=\frac{\mu_smg}{k}$$ which is the distance the spring can be stretched without the box moving when it is released.
We know $\mu_s=0.74, m=0.8kg$ and $k=59N/m$. Therefore, $$x=0.098m=9.8cm$$
