"He had had some problems."
Translation:Lui aveva avuto dei problemi.
Because 'ha avuto' = 'HAS had' not 'HAD had'. It'd be present perfect (the auxiliary is in the present tense + a past participle). 'Had had' is past perfect in which the auxiliary is in the simple past tense + a past participle and it's used to describe a past action that happened prior to some other past action. "He had had (or He'd had) some problems, before he won the lottery."
Laura, I believe it's because 'qualche' is always followed by a singular noun -- e.g. qualche giorno, qualche volta -- even though you'd translate it as a plural: a few days/ a few times. What you'd want here if you're going to use a plural noun is 'alcuni problemi' I believe. I'm not a native speaker so you might want to check that out, but I believe that's correct. Another point is there's no qualcho, qualcha, or qualchi. It's always qualche + a singular noun = a plural.
To make things even more confusing the DISTANT past perfect is covered by a tense that Duolingo doesn't teach--the trapassato remoto which uses the passato remoto form of avere/essere as the auxiliary. It would be ebbe avuto......You would probably only see this in literature or story telling. If anyone is interested here is a site that has easy to understand Italian fairy tales (translated) for free, and for a few bucks a month you can get audio as well. Thefablecottage.com
I would recommend a review of the English past perfect tense and when it is used as a first step. The trapassato prossimo will make more sense to English speakers if they understand the English past perfect tense first. I am not saying that applies in your case Lucas, but I have noticed that many people on this forum apparently do not use past perfect tense at all in their day-to-day English and so find the trapassato prossimo more difficult or even meaningless as a result.
The other complication with Italian that it uses either avere or essere as the auxiliary verb, and the inflection of the past participle, if any, depends on which auxiliary verb is being used for a particular verb and what the rules are for inflection of the participle based on either the subject or preceding direct object. It is therefore important to know what auxiliary a verb takes and what the rules are for the inflection of the participle when using that auxiliary. Generally a transitive verb takes avere and an intransitive verb takes essere, and some verbs take either according to whether it is used transitively or intransitively. The auxiliary for a particular verb can also be obtained from verb conjugators such as the following:
roman: thank you! I couldn't agree more. You've said it all very well. -- And I won't even get into why learning a foreign language's compound past tenses is so difficult for many Americans when you routinely hear things like "I could have (coulda) went, if she would have (woulda) came. Yes (Yeah) I shouldn't have (shouldn'ta) did that. But at least I seen her." Trust me it's not the foreign language in many cases that's difficult, it's the lack of understanding and awareness of how our own language works that's the problem.