The correct answer is B. That he cannot buy food for us. This sentence structure uses the correlative conjunction "so...that" to express a cause-and-effect relationship. The first part, "My father was so poor," describes the degree of his poverty (the cause). The "that" clause then introduces the consequence or result of that extreme poverty: "that he cannot buy food for us." This construction is grammatically sound and logically completes the thought.
Options A and C, "To get medical help for my mother" and "To send me to school," are incorrect because they use the infinitive "to." While "to" can express purpose, it doesn't fit the "so...that" structure. If the sentence were "My father was too poor to get medical help," it would be correct, but "so poor to" is ungrammatical in this context. The "so...that" construction specifically requires a clause following "that" to describe the outcome, making option B the only viable choice.