4x4 and 4x2 cars

4 by 4 cars means 4 wheel drive, in which all the 4 wheels are engaged to provide power to the move the vehicle.
4 by 2 cars means 2 wheel drive. In it 2 wheels are directed by the steering.
It may be Front Wheel Drive or Rear Wheel Drive.

4x2 means vehicle has 4 wheels but power is distributed to 2 wheels only. Means two wheels are driving and 2 wheels are driven. This is generally used in light vehicles. Drive may be front or rear wheel drive.

4x4 means all 4 wheels get power from engine. It may be partial 4 wheel drive or all wheel drive

In Partial 4 Wheel Drive, driver may manually switch between two-wheel-drive mode or streets and four-wheel-drive mode for low-traction conditions such as ice, mud, snow, or loose gravel.

4 wheel drive is mainly used in off-road vehicles and SUV's

you could place it in 2 ways:
Sedans,hatchbacks and kinda stuff.. these are mostly 4X2 kinda stuff. That means, out of 4, only 2 wheels are provided with power. This is usually done to the rear wheels. Cuz, that provides better torque and control as the front wheels are used for turning.Mostly commercial transport vehicles have this.
SUVs' and stuff, these have a 4x4 system. Good for hill climbing Most jeeps, military vehicles are designed under this as they need more maneoveurability. Now, here alll the 4 wheels recieve the power and hence it gives a good starting and climbing torque.

These days, sport mode cars combine both these systems for high performance.!