A person ( 40 kg ) manages to remain at rest between two vertical...

For the person to remain at rest, the net force acting on him in any direction must be zero.

Considering the horizontal direction, the only forces acting on the person are the normal reactions from the vertical walls:
1. Normal reaction $N_A$ from wall A acting towards the left.
2. Normal reaction $N_B$ from wall B acting towards the right.

For horizontal equilibrium, we must have:
$\sum F_x = 0$
$N_B - N_A = 0$
$N_A = N_B$

By Newton's third law, the normal force the person exerts on wall A is $F_A = N_A$, and the normal force he exerts on wall B is $F_B = N_B$.

Therefore, it directly follows that:
$F_A = F_B$