Answer
Rank the forces in ascending order: (c) - (a) - (b)
Work Step by Step
To move the box, any force has to surpass $f_s^{max}$. In other words, the required force $F$ to start the box sliding has to be such that $$F=f_s^{max}=\mu_sF_N$$
1) Case 1: the elevator is stationary
Here $F_N=m_{box}g$. So $F_1=\mu_sm_{box}g$
2) Case 2: the elevator is accelerating upward
The elevator accelerating upward means the upward force $F_N$ exceeds the downward one $m_{box}g$. According to Newton's 2nd law, $$F_N-m_{box}g=m_{box}a$$ $$F_N=m_{box}(g+a)$$
So $F_2=\mu_sm_{box}(g+a)$
3) Case 3: the elevator is accelerating downward
The elevator accelerating downward means the upward force $F_N$ is smaller than the downward one $m_{box}g$. According to Newton's 2nd law, $$m_{box}g-F_N=m_{box}a$$ $$F_N=m_{box}(g-a)$$
So $F_3=\mu_sm_{box}(g-a)$
Therefore, in short, we have $F_3\lt F_1\lt F_2$
