（ ）the door than somebody started knocking on it.

就选B
选C的话,要改一下No sooner had I closed
关门这个动作应该在started之前发生吧?
no sooner...than..."一...就..."
引导时间状语从句,主句用过去完成时,"than"后面的从句用一般过去时.(从这里可以知道,no sooner后面是主句;than后面是从句)
例:
I had no sooner reached home than it began to rain.
我一到家天就下起雨来
No sooner ...than...常放在句首,表示强调.这时主句要倒装.
例:No sooner had I reached home than it began to rain.