Answer
(a) The magnitude $f_s=267N$ and its direction is n the $+x$ one.
(b) The magnitude of the largest pushing force is $363.09N$.
Work Step by Step
(a) When the refrigerator still does not move, the static frictional force $f_s$ acts on the refrigerator with a magnitude equal with that of the pushing force $F$ but in the opposite direction.
$$\vec{f_s}=-\vec{F}$$
Therefore, in magnitude, $f_s=F=267N$ but its direction is in the $+x$ direction.
(b) $F_{max}$ before the refrigerator starts to move equals $f_s^{max}$
Therefore, $$F_{max}=\mu_s\times F_N$$
We have coefficient of static friction $\mu_s=0.65$ and $F_N=mg=57\times9.8=558.6N$
$$F_{max}=363.09N$$
