Every action has an equal and opposite reaction. This is why the picture shown above would not result in motion of the wall. The action is the force on the wall made by the hand, and the reaction is the force of the wall on the hand. These two forces are balanced, causing no change in motion.
force of hand pushing against the blue wall
force of wall pushing against hand
Newton's Third Law can also be shown with moving objects. If these two blue spheres are travelling at the same speed in exact opposite directions, that would be the action. Both spheres would continue moving until...
...they collide! The two spheres would continue moving towards each other until they collided. Then, the two spheres will have an equal and opposite reaction and start moving in the opposite direction of their first.