Translation:She will have taken the medicine to the hospital.
Yep, I made the same mistake before I took a step back and realized that "taking a pill" is an English idiomatic expression, not a Spanish one. If they meant to refer to her swallowing a pill, they would have used tomar, not llevar. Learning not to think in English is the hardest part, really...
On the contrary, you have to think very carefully about the ins and outs of English. In this case, you have to consider how the verb "take" can take on different meanings depending on what preposition follows it. There in that last sentence I have given it another meaning with "take on".
As a nurse, this sentence makes perfect sense to me. I appreciate it when a patient brings their own medication to the hospital in order to verify the names/dosages of the pills that s/he is taking in order to get them properly accounted for on their hospital medical record (much easier than them saying "I take the purple one for my stomach once a day and the white one for my blood pressure twice a day"). Once that is done, the medications are then sent back home with the family.
I think they're nice about "typos" in Spanish (which is my case were probably just wrong" but not in English. They have caught me time and again writing "the" instead of "they" when I missed the y in typing - a real typo. That really irritates me. It just happened in this lesson!