The correct factorization of this equation is (2y - 8)(x + 4).
In order to factor polynomials with 4 terms like this, you can often use a strategy called grouping. To do that, split into two different binomials.
(2xy + 8y) and (-8x - 32)
Now you can factor out the greatest common factor of each parenthesis.
2y(x + 4) and -8(x + 4)
Now in grouping, if after factoring out the greatest common factor, you can put the two things you pulled out in one parenthesis. You can multiply that by one of the matching set for the final answer.
(2y - 8)(x + 4)