What is the answer to this infamous "Common Core" question?

This "infamous" question is so poorly worded, but any mathematical answer that can be given would reinforce the perception that "the question is OK, see, it has a valid answer!"

The question is not OK.

Word problems should not be about mulling over "what did the author want to say?". Even the "trick" questions are normally about spotting some well-defined linguistic (or mathematical) trick, rather than based on complete lack of clarity. Plus, note it was not meant to be a trick question, but some standard question meant to assess how well students of certain age comprehend divisibility and common multipliers.

I can personally think about a dozen different ways to write a word problem which would boil down to the same mathematical problem and will be better worded.

As for this question, I hope if it was on some exam, that it did not affect anyone's passing or failure. I can relate to a poor methodical soul who got stuck for two hours on that question, trying to get their head around it and failing to comprehend it (and also wasting precious time for the following questions) not realising that it is not their fault.

The difficulty arises from the confusing wording and strange premise. Juanita is buying "stickers", not "bags of stickers". Each friend is to receive a single bag of stickers, with the number of stickers in each bag the same. For reasons unexplained, Juanita does not know exactly how many friends she is giving stickers to, but she does know that it is either $4$ or $6$. Thus, the question is how many stickers to buy so that she will be able to divide them evenly among the friends, whether there turn out to be $4$ or $6$ of them. The answer, then, is any multiple of both $4$ and $6$. Equivalently, the number of stickers can be any multiple of $12$, which is the least common multiple of $4$ and $6$.

Juanita buys zero bags. Then she gives zero to each friend. After that, there are zero stickers left over.

(Note that, consistent with other answers, zero is a multiple of twelve.)

Beyond that, I keep wondering how many bags of stickers Juanita intends to keep for herself after supplying her friends with some. It may well be that there are no circumstances under which there would be any "left over".