Yeah answer is 0. I have done this question with literally hundreds of people and almost everyone starts by factoring the quadratic (and assuming that it equals 0 even though the quadratic is what they are asking for and not what they are giving as a fact). They then get x= -4 and x=1 and don’t know what to do with the 2 “answers.” At that point most people then realize that the question is asking for the quadratic not for x so they usually then proceed to plug -4 and 1 into the quadratic and with some relief then see that the output is 0 in both cases and then conclude that the answer is 0. It’s at this point that I usually point out to them that although they got lucky and got the question correct, the only reason that they got the quadratic to equal 0 is because they assumed it was 0 in the first place! Again it plays with people’s tendency to regurgitate what they learned in school and in most cases in school the quadratic is set to equal 0 and you are solving for x.
It’s a great teaching question because it illustrates so many things, but one very fundamental thing that it illustrates is the need to parse the question into the given facts on the one hand and the question that they are asking you to solve for on the other. That seems so basic but so many people fail to do it, especially on a question like this. Obviously the If (4-x) / (2+x) = x is the given fact so if you are trying to answer the question by completely ignoring the only given fact, then you are unlikely to be able to get to the answer.
The other great thing that it teaches is to pay attention to what the question is actually asking for. The other inefficient thing that many people do on this question is to manipulate the given fact (the (4-x) / (2+x) = x), get everything on one side of the equation, and then solve for x (by factoring the quadratic). They then plug the 2 values of x into what the question is asking for without ever realizing that they had x^2 + 3x - 4 = 0 in like the second step of the process. They were just so blind to what the question was asking for that they never noticed it and took the many extra steps of factoring the quadratic, solving for x, and then plugging the values of x back into that very same quadratic.
Great teaching question in my opinion. And very similar to the one that the OP was referencing.