We get the left side into the form of a "monic trinomial"

x² + Bx + C = 0

and use the theorem that B is the opposite of the sum of 
the roots and C is the product of the roots.

h - 8x - 2x² = 0

We rearrange the left side in descending order:

-2x² - 8x + h = 0

Then we divide every term by -2

-2x²    8x     h     0
———— - ———— + ——— = ———
 -2     -2    -2    -2
               h 
    x² + 4x - ——— = 0
               2

We first determine the other zero by using the fact that
the coefficient of x, which is +4 is the sum of the roots with
the opposite sign.  If the roots are r1 and r2,
then  

r1 + r2 = -4  (which is +4 with the opposite sign).

We are told that r1 = -2, so we substitute that and get:

-2 + r2 = -4
     r2 = -2

So both roots are the same.  Now the last term of the "monic trinomial"
is the product of the roots, therefore

               h 
            - ——— = (-2)(-2)
               2

               h 
            - ——— = 4
               2

               -h = 8

                h = -8.

Checking:

  h - 8x - 2x² = 0
 
 -8 - 8x - 2x² = 0

 -2x² - 8x - 8 = 0

   x² + 4x + 4 = 0

(x + 2)(x + 2) = 0

x + 2 =  0;  x + 2 =  0
    x = -2;      x = -2 

So it checks. h = -8

Edwin