Translation:What is that country's name?
In contexts where the difference between "the" and "that" is not important, その can be translated as "the". Sometimes either works, but one may make more sense than the other. Sometimes, existing convention makes the choice obvious.
e.g. (on a game show) その答えは!? And the answer is!?
Also note that "and" appeared from nowhere because of the convention in English. Even for very closely related words, it's rare that you can do a simple word replacement and expect it to work for all cases.
I agree with what is said by Akira with on exception. In English we usually us the oarticle "the" to show specificity, but in tbis case "that" leave no question in the mind of the person being questioned. For this to be "the" i would have to assume that a previous discussion happened and i was being asked again about that specific country we had talked about. A cold question about the name of a certain cointey i would use the word "that."
Is there really no way to get 何 to be read as NAN instead of NANI? It's not a problem for me, but beginners in Japanese who try Duolingo are constantly subjected to the wrong pronunciation of the kanji, and often it's much worse than NAN vs. NANI. There must be a way for the computer experts at Duolingo to tag the kanji with the correct pronunciation, according to the context. Until that happens, I'm advising my beginning students to turn off the sound when working with Duolingo in Japanese.