Question

When do action and reaction forces within a system not cancel each other?

Answer 1

Action and reaction forces do not cancel each other; if they did, no motion
would ever be possible, since for every action there is an equal and opposite
reaction. This means that for example, when my hand pushes on a door, the door
is also pushing on my hand, with equal force and in an opposite direction.
Nonetheless, the door still moves.