Step 1: A rocket burns fuel and pushes hot gases out of its rear nozzle at high speed.
Step 2: Before the gas is ejected, the total momentum of the rocket and fuel system has some fixed value, possibly zero if it starts at rest. No external horizontal force acts on the system during this short burn.
Step 3: Since the gas is pushed backward carrying momentum, the rocket must gain an equal and opposite momentum forward, so the total momentum of the system stays unchanged. This is exactly the law of conservation of linear momentum, and it is the same idea behind the recoil of a gun.
The correct answer is option C.