Translation:Neither she nor he uses your telephone.
As a matter of fact, a great many, if not most, Americans say "use" rather than "uses" in this construction. I reflexively wrote "use" and it took me a while to see what Duo was objecting to. I tried the English sentence on my wife and she said "use" as well. Duo's grammar makes sense but usage at least allows "use."
Brit here and "use" is standard for us, too. Actually, it's more correct because "she nor he" reduces to "they", exactly as SanDigital has mentioned below. This hasn't been fixed for such a long time: I first encountered this discussion thread several months ago! I understand that there's only very few volunteers working on the Việt tree though. Please ensure to report these errors, not just comment about them, because the comments are not the right place to sumbit reports for changes and errors.
Không phải cô ấy, mà cũng không phải anh ấy dùng điện thoại của bạn.
- Neither she nor he uses your telephone.
In my knowledge, the main noun classifier is not mandatory with a possessive and/or a demonstrative determiner with it (see this discussion).
In such cases, your translation with classifier should be listed as acceptable. If you are buzzed, report it, Stewart, but I'm afraid it will not be added very soon, because the VN course seems to be paused: only our precious volunteer chị Huyền is still around, but she cannot see everything. So we may try to help each others.
Sometimes the element cái acts like a focus marker or emphasis marker (mostly negative connotations) and not really as a classifier.
I'd skip cái in this example (if not, I'd rather use máy = the machine, engine, device classifier instead), because in my understanding, the point in the sentence is not something about the phone itself, it is the fact that neither she nor he use it. By saying cái điện thoại của bạn you are not simply adding a determiner the (as such doesn't really exist in Vietnamese, it is much more abstract than in English), you are also expressing the somehow relevance of the related noun (i.e. . your very telephone/the very telephone of yours). I, for my part, miss this relevance here, so I would omit it.
And, please, I am always grateful to natives or contributors for clearing or correcting my comments resulting from research through the web and contents I have at home. I am really fond of Vietnamese and despite a few years studying experience there, I am now merely autodidact!
Cảm ơn rất nhiều!