Which analogy can best be likened to the activation energy of a chemical reaction? a drain through which water flows a slide down which a child descends a hill over which a wagon is pushed an alley down which a bowling ball is rolled?

Answer is: a hill over which a wagon is pushed.
For all chemical reaction some energy is required and that energy is called activation energy (energy that needs to be absorbed for a chemical reaction to start).
There are two types of reaction: endothermic reaction (chemical reaction that absorbs more energy than it releases) and exothermic reaction (chemical reaction that releases more energy than it absorbs).
Reactions occur faster with a catalyst because they require less activation energy.