Newton's third law of motion states that for every action, there is an equal and opposite reaction. This implies that when one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first object.
Among the statements you've provided, the one that is always correct according to Newton's third law is:
"If a moving object hits another object, then the second object will push back."
This statement accurately reflects the principle of action and reaction, indicating that both objects exert forces on each other during the collision. The other statements aren't universally true: the second object doesn't necessarily start moving (it might not move if it is immovable or if the first object doesn't have enough force), and it's also not true that both objects will stop moving (they might continue moving after the collision, depending on their masses and velocities).