Државе немачког говорног подручја

You could have figured out Germany, it's in the title(Nemacka)

Yes and no. In Russian, the language (Немецкий) and the country (Германия) have totally different words. My initial incorrect assumption was that it would be similar in Serbian.

Could I have thought (semi-) laterally about it for a bit and tried something like Немачка? Sure. But with only one minute on the clock, I was running out of time super fast. And once Австрия and Германия (plus a few attempts at expected substitutions, e.g.: "jа" for "я") didn't work, I was pretty much out of time anyway.

Looking over the answers again, I notice that Луксембург is only one letter away from the Russian Люксембург. And it's a relatively intuitive substitution. So that's the one that I probably had the best shot at guessing. But I didn't. Ah well.