2 | 1   -b      4   -20
  |      2   4-2b   16-4b 
    1   2-b  8-2b   -4-4b

The remainder is -4-4b and it must equal to -2,
so we set the remainder equal to -2:

                -4-4b = -2
                +4      +4
                ----------
                  -4b = 2

                  
                    b = 

Edwin

Apply the Remainder theorem.


The remainder theorem says that  


    if a polynomial f(x) is divided by a binomial (x-a), where "a" is a constant term (a number), 
    then the remainder is equal to the value of f(x) at x= a, i.e. f(a).


In your case  a = 2.  By y substituting x= 2 into f(x) you get

    f(2) = 2^3 -b*2^2 + 4*2 - 20 = 8 - 4b + 8 - 20 = -4b - 4.


Therefore, your equation to find "b" is

    -4b - 4 = -2    (since -2 is the remainder !)

which implies  4b = 2 - 4 = -2,   b =  = -0.5.