First, roll the car across the floor [floor tiles are better for this purpose than floor carpet], and see that it goes on a virtually straight path. Then, use the clay to lock the rear wheels to the auto frame, so that the rear wheels will not rotate. When the car is then rolled across the floor, it tends to "fish tail" out of control, and in fact if there is enough room the car will rotate so that the rear of the car ends up in front.
In other words, if the rear wheels are locked and the front wheels are not, the car is unstable and likely to spin around and out of control. To illustrate this point, push the car across the floor with the rear end [locked wheels] in front, and observe that the car is stable when going backwards.
As a variation, you can lock the front wheels with the clay, and observe the car goes forward rather well, but tends to "spin out" when going backwards.
The effect is caused by the fact that the rolling front wheels are instantaneously at rest with respect to the ground at the point of contact, whereas the rear wheels are sliding over the ground [kinetic friction is present]. Kinetic friction is always less than static friction, and the force/torque imbalance produces an instability. For essentially the same reason, you get more traction [on ice, snow, mud, or whatever] if you avoid spinning the wheels of the car.
This exercise illustrates several points in automotive engineering: