If the function y = {y1, y2 is to be considered continuous, then the value of y1, at x = -4, must be equal to the value of y2, at x = -4.
y1 = b - 2(-4) = b + 8
y2 = (-96)/(-4 - b)
Since y1 = y2, then
b + 8 = (-96)/(-4 - b)
(b + 8)(-4 - b) = -96
-4b - b^2 - 32 - 8b = -96
b^2 + 12b - 64 = 0
(b - 4)(b + 16) = 0
The function y is continous if b = 4, or b = 16
It it's a truth set that you are looking for, then the truth set is: b = {4, 16}