A girl jumps forward off of her skateboard. The skateboard weighs much less than the girl. [Friction in the wheels and between the wheels and the ground is so small that you don't need to consider it.] How does the force on the girl compare to that on the skate board?

We can think that the girl is initial over the skateboard, when she jumps forward, most of the force that she applies is downwards, so the force is transmitted from the skateboard to the ground.

Now, as she jumps forward, there is also some force applied in the horizontal direction, this force will affect the skateboard, accelerating it in the opposite direction (backward).

As the skateboard is way less heavy than the girl, the acceleration that the skateboard experiences will be bigger. Now, we can not estimate how much the skateboard moves, because we do not know the initial velocity of the skateboard.