Answer
$(y+2)(y-2)(a-4)$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $ay^2-4a-4y^2+16=\\=a(y^2-4)-4(y^2-4)\\=(y^2-4)(a-4)\\=(y^2-2^2)(a-4)\\=(y+2)(y-2)(a-4)$