The wagon therefore exerts the same amount of force on the donkey (force towards the opposite direction). Thus, obeying the 3rd Law of Motion according to Newto

Question

Suppose a donkey pulls a wagon with a certain amount of force towards one direction. The wagon therefore exerts the same amount of force on the donkey (force towards the opposite direction). Thus, obeying the 3rd Law of Motion according to Newton; the forces cancel out and wagon-donkey system will not be set in motion. So how the horse pulls the wagon exerts the same amount of force on the donkey towards the opposite direction?

Answer 1

Newton's 2nd law says the system will accelerate in the direction of the net force.  While it is true that the donkey and wagon pull each other with equal and opposite forces, there is an additional force, the traction between the feet of the donkey and the ground.  When you consider the traction force, then you have a net force that will allow the donkey and wagon system to accelerate.