Find a nonzero vector normal to the plane z-4(x-4)=-4(5-y).

I rewrote it as 36=4y-z+4x to find the normal and got the normal vector (or the gradient?) [4, 4, -1] but that isn't the right answer. I'm not sure what to do. Thanks for the help in advance!

I think the answer you have is right. It's the normal vector by the way.
There are actually infinitely many answers to this. <-4, -4, 1> is another answer. Also <1, 1, -1/4>.
But the answer you have is fine.

Hope this helps.