In the given sentence, the two events are: (1) The mariner set the sails; and (2) It began to rain. The second event happened immediately after the first.
If there are two activities or events and the second event occurs immediately after the first, we can express the same using the conjunction, 'No sooner... than'. The phrase, 'No sooner' introduces the first event. This is already given in the sentence. The word, 'than' introduces the second event. Hence, the most appropriate conjunction to fill the blank and precede the second event (It began to rain) is, ' than'. Option B is the correct answer.
Option A: The word 'then' when used alone (without the word, 'If) in a sentence is an adverb, which means 'at that time'. Hence, this is not the correct answer.
Option C: When the word 'then' is used alone in a sentence (i.e. without the word, 'If), it acts an adverb of time and means ' at that time'. It cannot be used in a sentence when the conjunction, 'No sooner' is used. The appropriate way of using it is: 'When the mariner set the sails, it began to rain'. Hence, option C is incorrect.
Option D: The word 'after' is a conjunction which means, 'during the period of time following (an event)'. It cannot be used in a sentence when the conjunction, 'No sooner' is used. The appropriate way of using it is: 'After the mariner set the sails, it began to rain'. Hence, option D is incorrect.