According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
[tex](a+b)\cdot(c+d)=ac+ad+bc+bd[/tex]Using this property in our product
[tex](y-4x)(y^2+4y+16)[/tex]we're going to have
[tex](y-4x)(y^2+4y+16)=y^3+4y^2+16y-4xy^2-16xy-64x[/tex]Comparing this expression to the expression given, we have the value of a.
[tex]\begin{gathered} y^3+4y^2+ay-4xy^2-axy-64x=y^3+4y^2+16y-4xy^2-16xy-64x \\ \Rightarrow a=16 \end{gathered}[/tex]