it says "your" coffee, not the coffee
check this it will help you understand http://duolingo.com/#/comment/317859
In short, we can omit possessives (mia, suo, tuo..) if it agrees with the person
Why can't "senza lo zucchero" be used? Why is the article sometimes used and sometimes not in cases like this where we say "sugar" and not "the sugar"?
could it also be: di prendere il caffè senza zucchero
i still don't get it why wouldn't it be, prendi il tuo caffe senza zucchero