"The farmer has horses."
Translation:Çiftçinin atları var.
It's not the accusative. It's the possessive form.
atlar (horses) → atları (the horses [accusative])
atları (his horses] → atlarını (his horses [accusative])
Yes, when a word ends in a consonant, the accusative and the 3rd person possessive look the same. You can only understand it from the context.
Simply using "atlar" is out of the question since we have "çiftçinin" (of the farmer). So something is owned here. In Turkish, it's never enough to say "the horses of the farmer". You actually both have to say "of the farmer" and then indicate that they're "his" a second time. So, çiftçinin atları = Of the farmer his horses → The horses of the farmer.
But using the logic Duolingo is using it is veru confusing. It should be The farmer has his horses. Or something like that. I feel that Duolingo confuses a lot of grammar issues and makes it unnecessarily complicated. I think the English translation should somehow indicate the horses are his to show that you need to use the endings discussed above.
If we did that, you would see hundreds of posts complaining "This is not idiomatic English!" or asking "Well, if this is 'the farmer has HIS horses', how do we simply say 'he has horses' without the "his" bit?" It would be even more confusing. Just learn that this is how it is said in Turkish.