Hardly _______ I shut the door when the telephone rang.

The correct completion for the sentence is:

"Hardly had I shut the door when the telephone rang."

Explanation:

This sentence is an example of inversion, where the auxiliary verb comes before the subject. In this case, "hardly" is a negative adverb of frequency, and when it is used at the beginning of a sentence, it requires inversion.

a) have: "Hardly have I shut the door when the telephone rang." - This option is grammatically incorrect. The correct auxiliary verb is "had" for inversion.

b) did: "Hardly did I shut the door when the telephone rang." - This option is grammatically correct, but the use of "did" in this context is less common. The more appropriate auxiliary verb is "had."

c) could: "Hardly could I shut the door when the telephone rang." - This option is grammatically correct, but the use of "could" may imply a sense of ability or possibility, which might not convey the intended meaning, hence not the correct answer.

d) had: "Hardly had I shut the door when the telephone rang." - This is the correct option. It maintains proper inversion, indicating that the action of shutting the door was immediately followed by the ringing of the telephone.