Question

You___ the cleaning I would have done it tonight. ( a )couldn't have done (b)-needn't have done (c)can't have done (d) wouldn't have done​

Answer 1

You wouldn't have done​  the cleaning.

Answer 2

Answer:

You needn't have done the cleaning I would have done it tonight.

Explanation:

Need not is a modal that means something is/was not necessary.  

Example

You need not come to the office on Sunday.

‘Needn't’ is a modal verb. There are some other modal verbs such as could, may, might, must, shall, should, will, and would. These verbs are used to express possibility, permission, ability, request, offer, suggestion, wishes, etc. In Simple conjugation only bare infinitive is used with them. For example, ‘She can run fast.’ (modal+ v1).  

The formation of conjugations using the modal auxiliaries can be summarized as follows:

I am using only modal ‘can’ for explanation. The same rules apply for other modals as well.

Conjugation Modal Auxiliary Verb Form

 Simple   can   bare infinitive (v1)

 Continuous   can + be   present participle (v1+ing)

 Perfect   can + have   past participle (v3)

 Perfect Continuous   can+ have been   present participle (v1+ing)