If a boy is stationary on a skateboard and jumps off forwards, why does the skateboard move backwards?

Momentum before the collision or separation must equal the momentum afterwards, this is called the conservation of momentum. The situation before had the skateboarder on the skateboard, both stationary. As momentum is the product of mass x velocity, and we know from the question stating they are stationary, that the velocity must be zero. If you multiply anything by zero you get zero. So the momentum must equal zero at the start. This also means that the momentum must equal zero after he jumps off the skateboard. If you jump off a skateboard forwards what happens to your momentum? By moving forward you must have a speed, or velocity, and everyone and everything has a mass, so if neither of these are zero, we must have a momentum. As momentum is a vector (so has an amount AND a direction) we must assign a direction to this value. So we'll use the direction given in the question; forward. We know that the overall momentum afterwards must equal the momentum of the skate board + the momentum of the boy. If we know this equals zero overall and we have a positive value for one (the boy), we know that the other must be a equal but negative value. (Eg. 0 = 4 + x, so x must be -4). So as we want to make this negative, we want to put it in the opposite direction as the boy jumping. So this would mean the skateboard will roll backwards with the same momentum as the boy jumping off.