To answer this question, we need to understand the meaning and usage of each option.
Option A) "For" - This option is incorrect because it does not convey the correct meaning in the given context. "For" is typically used to indicate a purpose or duration, but it does not fit in the sentence "The students went home ___ school."
Option B) "After" - This option is correct. "After" indicates the sequence of events, implying that the students went home following their time at school. The sentence "The students went home after school" is grammatically and contextually correct.
Option C) "Since" - This option is incorrect because "since" is used to indicate a point in time or a specific event that serves as a starting point for another event. It does not fit in the sentence "The students went home ___ school."
Option D) "None of these" - This option is incorrect because option B, "After," is the correct answer.
Therefore, the correct answer is option B, "After." This option is correct because it accurately conveys the sequence of events, indicating that the students went home following their time at school.