avait vs. aurait?

Question

I don't understand why this sentence could have is avait pu, where in no. 4 the answer is aurait pu, both meaning "could have"

Maarten Kamp · Accepted Answer

Kathryn, 
it would help if you can find and add the 2 questions in full as this would allow a specific answer based on the context. 
However,  ‘ could (have) ‘ has different meanings in English - modal, conditional or past tense of the verb ‘ can ‘. 
In French those different meanings are conveyed with different conjugations of pouvoir (usually) - in compound tenses that requires different forms of the auxiliary ‘ avoir ‘ preceding the past participle ‘ pu ‘.
The links below are helpful in understanding what the differences are, and how that impacts usage and translation :
https://englishlive.ef.com/en/blog/language-lab/use-should-would-could/
 https://www.lawlessfrench.com/grammar/pouvoir-lesson/
 https://www.lawlessfrench.com/grammar/compound-modal-verbs/
 https://www.lawlessfrench.com/grammar/modal-verbs/ 
 https://www.lawlessfrench.com/verb-conjugations/pouvoir/

al soboleva · Answer

'aurait' is conditional and 'avait' is not, 'avait pu' is past indicative and would simply translate to smth like 'had been able to', whereas 'aurait pu' has the meaning of 'might have had', 'could have'