In short
Newton's third law says that when one object pushes on a second object, the second object pushes back on the first with a force of equal size in the opposite direction.
The two forces act on different objects, so they never cancel each other. A rocket pushes gas backwards and the gas pushes the rocket forwards. You push the ground backwards when you walk and the ground pushes you forwards. The third law is the reason that momentum is conserved when two objects interact.
A skater pushes a wall with a force of . The wall pushes the skater with in the opposite direction, so the skater moves away from the wall.
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