The hens . . . . . . . . into the house if you had shut the door.

The sentence "The hens would not have got into the house if you had shut the door." is a conditional sentence that expresses a hypothetical situation in the past. It uses the third conditional form, which requires the past perfect tense in the if-clause ("if you had shut the door") and the conditional perfect tense in the main clause ("would not have got").

In Option B, "did not get" (simple past) does not fit the conditional structure of the sentence.
In Option C, "does not get" (present tense) is not appropriate for describing a hypothetical past situation.
In Option D, "not got" (incorrect form) is grammatically incorrect and does not fit the structure of the sentence.

The correct answer is Option A: would not have got, which accurately conveys the third conditional structure and the hypothetical situation described in the sentence.