The correct answer is A. close.
The verb “close” is the most common and natural way to complete the sentence “Would you . . . . . . . the window?”. The other options are not grammatically correct or do not make sense in the context of the sentence.
Option B, “to close”, is the infinitive form of the verb “close”. It is not typically used in this context.
Option C, “closed”, is the past tense form of the verb “close”. It is not typically used in this context, as the sentence is asking for a future action.
Option D, “closing”, is the present participle form of the verb “close”. It is not typically used in this context, as the sentence is asking for a single action, not an ongoing action.