If action is always equal to the reaction, explain how a horse can pull a cart.

Explanation

It is true that when a horse pulls a cart with a certain force, then the cart also pulls the horse with the same force and the system of horse and cart should not move.
However, if we analyse the problems carefully, then horse not only applies force on the cart, but also pushes the earth backwards with its feet. In this action of the horse, the earth reacts back and pushes it in the forward direction. Now, the force applied by the horse on the earth is insufficient to move the earth, but the force applied by the earth is sufficient to make the horse to move in the forward direction. It is the unbalanced force applied by the earth, on the horse which makes the system of horse and cart move in forward direction.