It seems there is an error in the 3rd example. The rule is, take each figure from left to right and stack each under the previous one. For L and J shapes the top cell is stripped. The L shape dictates that the next shape will be shifted one cell to the right, the J shape tells the next figure to shift to the left.
If all examples are right, then the rule is more complicated than that, involving rotating L clockwise, J counterclockwise. Authors claim that it should be solvable by children, then the rule must be simple.