Answer
$\mu_s = 0.46$
Work Step by Step
The drawer will start to slide when the applied force $F$ is just enough to overcome the force of static friction.
$F_f = F$
$mg \mu_s = F$
$\mu_s = \frac{F}{mg}$
$\mu_s = \frac{9.0 ~N}{(2.0 ~kg)(9.8 ~m/s^2)}$
$\mu_s = 0.46$
The coefficient of static friction $\mu_s$ between the drawer and the cabinet is 0.46.
