Consider the situation shown in the figure. Suppose all the...

Let us consider the forces acting on block $B$ in the vertical direction.

Since the entire system is in equilibrium, block $B$ is also in equilibrium. This means the net vertical force on block $B$ must be zero.

The gravitational force acting on block $B$ is its weight ($m_B g$), which pulls it downwards.

To balance this downward force, there must be an equal upward force. The only surface in contact with $B$ that can provide this vertical force is the surface of block $A$. Thus, the static frictional force exerted by $A$ on $B$ must act in the upward direction.

Therefore, the friction on $B$ due to $A$ is upward.