It is asking: if you start with a very large mass and slowly decrease the mass, what would the mass be just before the pull of that rope finally gets it to move?
You asked: You asked: "Isn't there only one solution (mass) to this question?" No. You are visualizing an equation that would yield the mass. But, if you doubled the mass, could I not be even more confident of it remaining at rest? More normal force, the more the friction, right?
You know that a very large mass would not move because of that 28 N pull. You also know that a very small mass would easily move because of that 28 N pull. There is an amount of mass, between those you visualized, for which it would not move - but be just barely hanging on. That is the smallest possible mass.
I have answered your question. But if you still need help finding that mass, message me.
P.S. Remember that the angle of that rope will partially lift the mass decreasing the value of the normal force.