The "illegal" (sometimes called "excluded") values of b are those values of b that would make the denominator equal zero. So, we set the denominator equal to zero and solve for b.
denominator = b² - 2b -8 ⇒⇒⇒ by factoring
∴ b² - 2b -8 = 0
(b-4)(b+2) = 0
b - 4 = 0 or b + 2 = 0
∴ b = 4 or -2
the illegal values of b in the fraction = -2 , 4