Translation:We would have it.
I speak 3 Languages fluently. Native persian speaker, Urdu and English. And would like to say that English has been the easiest and most logical of the 3 Languages that I have learned. Not comparing to persian as I was born in that language and have completely forgotten how difficult it was.
For French conditional, notice that the stem is like that of the future tense, but the ending conjugations are those of the imperfect tense:
"serais" is like "SERai" + "étAIS" for "être"
"aurais" is like "AURai + avAIS" for "avoir"
"ferais" is like "FERai" + "faisAIS" for "faire"
The same is true for the other "persons", too, not just first person singular. There are exceptions, naturally, but this is a pretty solid pattern.
I'm sure there are exceptions, but generally speaking, the conditional tense is very similar to the simple future. The stem is the same ( which most often but not always of course, is the infinitive form of the verb) but the endings, instead of -ai,-as,-a,-ons,-ez, and -ont are -ais, -ais, -ait, -ions, -iez, and -aient.
Basically, the correct translation to "Nous l'aurions" is "We would have it", and the translation to "We would have had it" is "Nous l'aurions eu".
I guess Duolingo gave you that answer by mistakenly combining would and have in the wrong context. Since "aurions" is in conditional (which generally translates to "would [verb]"), it means "would have" (therefore "Nous l'aurions" is "We would have").
"We would have had it" would be "Nous l'aurions eu"; this is a tense called "passé conditionnel", and it makes phrases like "would have been", "would have done", etc. Since the past participle of avoir is "eu" which means "had", you can just add that into "Nous l'aurions" to make "Nous l'aurions eu".
Hope that's clear enough (please, let me know if it's not)!
Oh, no. It is the dreaded -let's contract "have" everywhere- algorithm. The answer you were given is wrong. You know it; we know it. But unfortunately the person who programmed the computer doesn't know it. So we're stuck with it. All we can do is try to ignore it. In the meantime, the sentence "Nous l'aurions" is in present conditional (we would have it), not past conditional "nous l'aurions eu" (we would have had it).
The Tips and Notes have been written by the same people who have written the sentences in the course. So, lesson by lesson, the Tips and Notes are related to the very content of the course.
"Official grammar" can be found in many places (books or the internet) but none of these sources were written to match the course you get here.