When the car makes contact with the wall, a force (normal force) acts on the car, causing a deceleration. That’s what changes the speed of the car to 0 and does damage to the car. Newtons third law (equal and opposite reactions) explains what the wall feels (the same magnitude of force exerted on it – damaging the wall).
You can think of the same situation in terms of energy. A moving mass has energy (kinetic). When a force is applied to it, energy is transfered. In this case, the speed (and therefore the kinetic energy) goes to 0, so that energy is converted to other forms -which are observed in the aftermath of the crash (sound, friction heat, deformation of metal etc).
Forces cause energy transfer and change the state of motion of things
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