Answer
Staying at rest.
Work Step by Step
We have two probabilities here if the box is on the verge to slide down then the friction force will be up and if the box is on the verge to slide up then the friction force will be down.
So, the best way to answer this question is to find the friction force magnitude and direction that is needed to hold the box stationary and then compare it with the real friction here, the maximum (static friction force). If it exceeds the static friction force between the wooden wall and the wooden box, then the box will slide, and then we can define in which direction.
Let's start:
$$\sum F_x=F_n-12\cos30^\circ =0$$
$$F_n=12\cos30^\circ \tag 1$$
$$\sum F_y=12\sin30^\circ+f -mg=0$$
$$12\sin30^\circ+f =mg$$
Thus,
$$f =mg-12\sin30^\circ=1\cdot 9.8-12\sin30^\circ$$
$$f=3.6\;\rm N\tag 2$$
Now we need to find the real friction force here
$$f_{s }=\mu_sF_n = \mu_s 12\cos30^\circ $$
$$f_{s }=0.5\cdot 12\cos30^\circ =5.2\;\rm N$$
Now it is obvious that the static friction force is less than that needed above. And since the static friction force is greater than the force needed to hold it, so the box will not slide in any direction.
Therefore, the box remains stationary at rest.
