Instrumental (твори́тельный). The preposition «с» requires it. When used alone, itʼs usually translated «with» or «by», hence the name — it's used for instruments (я наре́зала хлеб ножо́м — I've cut the bread with the knife).
Hmm, some help here. If I understood this correctly, the instrumental case can be used with and without prepositions. And this sentence uses a preposition to denote that "I want coffee (but) with (my coffee, I also want) milk.
And if a sentence without the preposition "с" were possible, that would denote something like "I want (to make/create) coffee with milk (as my raw material).
We don't usually use instrumental case for raw materials. «Я хочу́ сде́лать ко́фе молоко́м» would mean 'I want to make coffee into milk' (i.e. transform coffee into milk), because instrumental case can also mean the result of the transformation.
Yes, of course, it would mean exactly this. Since ко́фе is indeclinable, all its cases look the same.
You could use subjunctive mood. It looks like the past tense, but has an additional particle «бы»: я хоте́л(а) бы... 'I would like'.
However, I don't think I'd use this when asking for something. If I'm ordering something in a café, I think adding «пожа́луста» gives enough politeness.
If I'm in someone's house, instead of telling my wishes, I'd ask about possibility: «мо́жно ко́фе?» 'is he coffee possible? can [I have some] coffee?'. «Я бы не отказа́лся/отказа́лась от ко́фе с молоко́м» 'I wouldn't refuse/mind coffee with milk' sounds pretty polite, too.
Perhaps your translation is not literal enough. It has a different structure: in English, you want milk with coffee, but in Russian, you want coffee with milk. The meaning is the same, but the sentence structure is not. I don’t know if this should be accepted.
Duolingo allows entering alternative translations. Wikipedia says that "white coffee" is used in some countries to mean "coffee with milk", so probably this is why the contributors added it.
Then, when you enter a sentence Duolingo doesn't have in the list of the translations, Duolingo tries to find the closest sentence and says "you should have said this". Usually it works:
- If someone entered "cafe with milk", Duolingo will correct it to "coffee with milk",
- if someone entered "white cafe", Duolingo will correct it to "white coffee".
This makes sense: Duolingo presents the sentence that it the most similar to the sentence your entered. If you just made a mistake in one word, it will show you the sentence with this word corrected, and not a sentence with a completely different structure.
However, this algorithm apparently doesn't try to move words around, it seems to compare words character-by-character. So, it compares your variant "milk with coffee" with the variants it knows like this:
- "milk with coffee" and "coffee with milk" = 10 mismatched characters,
- "milk w_ith coffee" and "____ white coffee" = 6 mismatched characters.
10 mis-matched characters is more to 6 mis-matched characters, so Duolingo arrives at the conclusion that you wanted to write "white coffee" and not "coffee with milk", and when displaying an accepted variant, it shows you this variant.
This is a problem in the algorithm. The algorithm can be improved, but since Duolingo is a proprietary closed-source platform, only the Duolingo management can do this, and we don’t know if they are planning to do this.