You can put this solution on YOUR website! "Illegal" values are those values of b which make the denominator of the fraction equal zero...it is forbidden to divide by zero, ya know...
so let's see what those values are...
b^2 - 2b - 8 = 0
(b - 4)(b + 2) = 0
b = 4 or b = -2
Thus we're not allowed to have b = 4 or b = -2...we say they are not in the domain of this expression...