Do you mean "dA", which is a scalar differential or " ", a vector differential? Since you are talking about the flux of a vector function through the surface, you must mean the latter and you want to find .
You can write the surface, z= 4- y as x= x, y= y, z= 4- y or as the vector equation . The derivatives, and lie in the tangent plane at each point and their cross product,
with "upward z component" or with "downward z component". Which of those you use depends upon how you want the surface oriented- whether you want to think of the flux as positive or negative.
Taking the "upward z compontent" so you have a sign wrong.