The correct answer is "any multiple of 12", but they really probably just want "12".
I agree that the question is poorly-worded, but after some reflection upon existing commentary and answers, I also agree it is possible to work out the proper mathematical problem and its possible solutions without requiring many leaps of logic or unfounded assumptions. However, I also believe that the actual answer to the question is not the answer that test reviewers would consider correct.
First, about how to solve the problem:
The first thing a student needs to do is eliminate what they don't need from the problem.
This is a common assessment objective of word problems - finding whether the student can determine what is or is not relevant to the question.
The scenario talks a lot about bags, stickers, and friends. We know that we need to fill bags with stickers, and the bags are being given to friends. We don't know how many friends Juanita has and, at first glance, this would seem to be part of the problem. However, the number of friends is irrelevant because Juanita has already narrowed the quantity of bags to two possibilities - 4 or 6.
Now the student can determine the mathematical problem, and its possible solutions.
We have either 4 or 6 bags to fill, and we want to buy an amount of stickers that divides evenly among the bags no matter which number is actually true. The easiest way to do this is to multiply the two numbers, for which you get 24.
It is important to note here that 24 is actually a valid answer to the question that has been presented to the student.
Now the student could conceivably extrapolate the ideal result, and determine that solution.
Considering that Juanita is buying these stickers, she probably doesn't want to pay more than necessary. And, if they understand the concept of the Least Common Multiple, the student could realize that there might be lower quantities of stickers that could satisfy Juanita's needs.
At this point, they would then do the appropriate work and arrive at the answer of 12 - which is probably the answer the instructors want to see on the standardized test.
The question as written leaves open the possibility of an infinite number of correct answers being considered "wrong".
That last part is where this question, in my opinion, fails to serve its purpose horribly. There's an important difference between this (from the original question):
How many stickers could she buy so there are no stickers left over?
And this (change in italics):
What's the fewest number of stickers she could buy so there are no stickers left over?
The former leaves all multiples of 12 as possible valid answers. In fact, the most correct answer would be for the student to write (as it's a free-form answer field anyway) "Any multiple of 12".
However, the latter form narrows the field of possibilities down to only the answer that costs the least amount of money. For that question, the only correct answer (assuming the stickers are individually priced, and there's no buy-one-get-one-free sales on) is 12.
A Better Question
Personally, I'd probably suggest a rewrite similar to this:
Juanita is going to the store to buy some stickers for her friends. To distribute them equally, she's going to put the stickers into bags. However, she left her bags at home and can't remember whether she has 4 or 6 bags to fill. She wants to be able to give the same number of stickers to each friend. How many stickers should she buy, to avoid spending any more money than she needs to while still equally dividing the stickers?
That puts the question in simpler terms, and links it to a practical real-life need (saving money), while keeping all of the elements from the original question.