To answer this question, we need to understand the correct usage of prepositions in different contexts.
Option A) For - This option is incorrect because "for" is used to indicate a duration of time, such as "for two hours" or "for a week." It is not appropriate to use "for" in this sentence to indicate the time the fire died out.
Option B) After - This option is correct. "After" is used to indicate a sequence of events, with the second event happening later than the first. In this sentence, "after" indicates that the fire died out later than nine o'clock.
Option C) Since - This option is incorrect. "Since" is used to indicate a starting point in time or a cause. It is not appropriate to use "since" in this sentence because it does not convey the meaning that the fire died out later than nine o'clock.
Option D) None of these - This option is incorrect because option B, "after," is the correct answer.
The correct answer is B) After. This option is correct because "after" correctly indicates that the fire died out later than nine o'clock.