You have to go in there and ____________ them! Without your encouragement and enthusiasm, I don't know what we would do.

The choice of "energize" is fitting in this context because it functions as a verb that conveys the action of giving energy or enthusiasm to others. Here, the sentence emphasizes the need for encouragement and enthusiasm, which aligns perfectly with the meaning of "energize."

In contrast, "energy" is a noun and would not grammatically fit the sentence structure that requires a verb. "Energetic" is an adjective used to describe someone or something that has a lot of energy, but it would not serve the purpose of expressing the action of motivating or invigorating others. Finally, "energetics" refers to the branch of science that deals with energy and its transformations, which is irrelevant to the context of providing encouragement. Thus, "energize" is the most appropriate choice to complete the sentence meaningfully.