You can tell me what could have been done.
Is this use correct? If it is can someone explain me part by part which parts of speech is used here and the construction.
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It is correct. Could is a modal verb. Have is an auxillary verb forming the perfect tense, with the past particple of "be", which is another auxillary verb, indicating the passive voice with the part participle "done" (p.p. of do)
The whole phrase "what could have been done" is a relative clause, and "what" means "that which".
So build it up:
I do something
Something is done (by me) (passive)
something can be done (with modal)
Something could have been done (modal in the perfect)
Tell me what could have been done. (as a subordinate clause)
You can tell me what could have been done (the original sentence)