"You have wine and he has milk."
Translation:Tu as du vin et il a du lait.
The first time you encountered "du," Duolingo should've presented you with this explanation (it did for me anyway): "The word du implies that the noun has no article, or it can be translated into some. For example, Je mange du pain translates into I am eating bread or I am eating some bread. Je mange le pain means I am eating the bread." In short, it is used for expressing "some," but it is also used where there is no article in English (such as this sentence). Hope that helps! More info can be found at http://french.about.com/od/grammar/a/articles_4.htm
Du/de la/des is a partitive article and should always be used when you are talking about foods you are taking/eating. Tu manges du poulet = You eat (some) chicken. If you use the, tu manges le poulet, you are talking about the concept of the food. You eat every chicken/the concept of chicken. You use the definite article, le/la/les, when you are talking about the foods you like. J'aime le poulet, because you like the concept of chicken.
That is truly weird. Using "have" in English that way is like saying, "I like to play the piano and basketball." If Duo gave you "Tu as du vin et il prend du lait" for "You have wine and he has milk", that would deserve an error report. Indeed, the French often use the verb "prendre" (to take) when referring to having something to eat or drink, but to mix them up in a sentence like this is just messing with you. The French sentence you give would be translated as, "You have wine (meaning you just have some, but you're not drinking it) and he is having milk (meaning he is drinking or is about to drink a glass of milk).
"Du" is what is called a partitive article. There are also definite articles and indefinite articles. "Du" is a contraction of "de + le" and is used before masculine nouns ("de la" is used for feminine nouns) when in English you might say "some". Often in English the word "some" is omitted. But even though you might omit it in English, if you could say it that way in English, then you will definitely use the partitive article in French. This can be a little tricky at first. Here are two links to help you:
"Le," "la," and "les" mean "the" in english, in masculine, feminine, and plural. "De" means "of." "De la" is feminine "of the" "Du" is a basically a shortening of "de le," and is the masculine "of the." "De le" is grammatically incorrect, so use du. "Des" is kinda like "de les," but like "de le," you MUST use the shortened version in order to be grammatically correct.