Does gearing down the car while going downhill damages car?

Gearing down the car while going downhill does not damage the car unless it's done improperly or in the wrong situations. When you shift into a lower gear going downhill, the engine's compression acts as a brake, helping to slow the car down. This can be useful for controlling your speed and reducing wear on your brakes.

However, downshifting at too high a speed or while the engine is revving too high can cause damage to the engine or transmission. It is generally best to downshift one gear at a time and to avoid downshifting into first gear unless you are coming to a stop.

Additionally, downshifting is not recommended in all situations. For example, if you are driving on a slippery road, downshifting can cause the wheels to lose traction and skid. In general, it is best to use downshifting as a supplemental braking method and not as the primary way to slow down or stop your car.