Wine is not really a word for which you can use "a". I think a glass of wine should be accepted too.

Hmm. In English, "a wine" means a variety of wine. If you order a drink at a restaurant, you would use "I'll have a glass of wine" or "I'll have some wine" or "I'll have wine", never "a wine". Does "en vin" refer only to a variety of wine? If not, then "a wine" is an incorrect translation. (I'm just learning Danish, so I don't know what "en vin" can be used for; but this exercise as is makes me think it refers to a variety of wine, and I don't think that's right.)