When no net external force acts on a system, the center-of-mass is stationary.
One or more parts of the system can move, but other parts must move in response to keep the center-of-mass in the same place.
A 90 kg man sits at one end of a 2.4 meter canoe that has a mass of 30 kg. If the man moves to the opposite end of the canoe, how far does the canoe move?