y² + 4y - 8x + 20 = 0

Isolate the terms in y on the left side:

          y² + 4y = 8x - 20

Multiply the coefficient of y, which is 4, by 1/2,
getting 2.  Then square 2. getting 4, and add +4
to both sides:

      y² + 4y + 4 = 8x - 20 + 4

Factor the left side, combine terms on the right:

   (y + 2)(y + 2) = 8x - 16

Write the left side as the square of a binomial
and factor out 8 on the right:

         (y + 2)² = 8(x - 2)

Write the 8 as 4*2

         (y + 8)² = 4*2(x - 2)

Compare to 

         (y - k)² = 4*a(x - h)

So -k = +8 or k = -8
   -h = -2 or h = 2
    a = 2

Edwin