Translation:We are drinking another cup of coffee.
Yes, I also wanted to ask what the difference between "ander" and "weiter" is, since the former means "other" as well. So, "Wir trinken eine weitere Tasse Kaffee", "Wir trinken eine andere Tasse Kaffee" and "Wir trinken noch eine Tasse Kaffee". Native speakers, help us with your powers!
I believe the difference is like what other answerers have mentioned (including you) i.e.
-weitere adj :— additional adj / more adj-
-andere pron :— other pron / another pron-
A sentence that combines the two words perhaps best illustrates this e.g.
.Weitere andere Reserven = .further other reserves OR
...sowie weitere andere Wagen dieser Bauart = ..as well as more other cars of this design type
Examples where one might use one and not the other :
..weitere Informationen finden Sie unter = ..see more information below [additional information expanding on the same topic but not some other information]
wenn andere Maßnahmen nicht ausreichen würden = when other measures would not suffice [with a different approach]
The difference in noch ein for one more (still) vs weitere for another is the same as that implied in English (if any-depends on context?).
There might be no difference in I want another cup of coffee vs. I want one more cup of coffee but there could be one depending on your intention/situation. The first one could mean some other variety of coffee if you're spoilt for choice (I want another one this time) -OR- it could mean another one of the same (in which case adding of the same at the end makes it clearer). One more implies just one and not anymore than that as well as implying the same exact order.
Aha, so, "Wir trinken eine weitere Tasse Kaffee" --> an additional cup, "Wir trinken eine andere Tasse Kaffee" --> another cup (as in, different, not this one) and "Wir trinken noch eine Tasse Kaffee" --> one more cup
The middle one is definitely different since it might be that you haven't drunk a single cup yet, you just want to drink eine andere because maybe the first one is wrong in some way. But what about "noch eine" and "weitere"? Both mean you already drank one cup and are proceeding to the next one. Is there any strong difference?
Is there another word used for "another" in German, or are you questioning which case you should be using? I haven't gotten this far, but "another" in this case seems like it is in the Accusative case, as the cup is the object being directly referred to by the verb "trinken".
Sometimes you lose hearts on guessing what Duolingo will consider the right answer. In such cases I try to translate word-to-word using what is given as hints. The English meaning for this sentence would be "we drink another (=one more) cup of coffee", but then the whole point of the exercise is to learn that "weiterer" is "further". So "We drink one further cup of coffee" was my best guess. But no, it had to be "we drink A further cup of coffee". Frustration...