There is something not quite usual in this locution; the only solution from those proposed is "Jaime les croissants avec du beurre." and so the test is quite right from the point of view of grammar and context. However, the context is quite rare. The usual locution is "croissant au beurre" (J'aime les croissants au beurre.). Croissants "au beurre" are croissants that are made using butter rather than some other type of fat. You can't say "avec du beurre" in this context.
If you were to say "avec du beurre" you would be talking about quite something else, something that a certain number of French people themselves might not undertand because it describes a practice that few people only know of or follow. It consists in splitting a croissant into two parts lengthwise and then spreading butter on the inside; you can spread it onto one only of the two pieces, then join the two parts together as a sandwich, and that definitely makes for a buttery taste. You can also spread the butter onto each side and eat them separately.
In this second (and rare) context the partitive makes sense then. Nevertheless, consider that in
- "Les croissants au (à le) beurre sont fabriqués avec du (de le) beurre."
you do use the partitive again when talking about what they are made with ( a certain amount out of the whole mass); it's the same idea as for the "croissant avec du beurre".
"De" here would mean "that are made out of butter", only butter or mostly butter: du pain de blé, de la farine de mais… Do you get it? You wouldn't have "avec" though: "des croissants de beurre". This, of course doesn't exit.
As you seemed to know about partitive in French, I assumed, however, that you knew about the contraction: "de le ==> du" for masculine nouns.