"The man does not drink the bad beer."
Translation:De man drinkt het slechte bier niet.
The girl does not drink cold coffee = Het meisje drinkt geen koude koffie (This is what Duo said was the right answer.) Yet now, De man drinkt het slechte bier niet.
Now that I've typed them both out, I can see that the difference is that cold coffee doesn't have an article, but the bad beer does. That is a very slight difference for such a major change in syntax and vocabulary.
I'm guessing that if it had been generally bad beer, as in The man doesn't drink bad beer (as a general rule, like the girl with cold coffee), then it would be De man drinkt geen slecht bier.
I suppose I just answered my own question. :)
No. "De man geen drinkt het slechte bier" is incorrect.
Because het is used, you cannot use geen, but you have to use niet to negate. You can think of geen as the negative form of een. Should you simply replace geen by niet then it's not correct yet, because the word order is incorrect.