"Are they taking good care of their twelve sheep?"
Translation:Starají se o svých dvanáct ovcí dobře?
I'm a little confused here, though I'm sure the explanation is simple. In the past we've had starat se o plus accusative to mean taking care of. However, here we have svých (genitive), dvanáct (accusative), and ovcí (genitive). If I had to take a stab I would say dvanáct is accusative because this expression is starat se o plus accusative. Ovcí is genitive because dvanáct is behaving like an adverb of quantity. And svých, because it is modifying ovcí has to be genitive, even though it is separated in the word order? It just seems so unnatural...
Your logic is very sound! Numbers above 4 take the genitive; since sheep are countable, here the noun and its modifier are both in the genitive plural, while the number itself remains in the accusative.
As a fellow learner, I'm often frustrated by word order, too. But I've seen this odd-seeming construction -- with an adjective or possessive in the genitive preceding a number in the accusative which is then followed by a noun in the genitive -- in some other sentences, so I’m beginning to get used to it! :-)