\[(y - 4)^{2} - (4 - y)(4 + y) =\]
\[= y^{2} - 8y + 16 - \left( 16 - y^{2} \right) =\]
\[= y^{2} - 8y + 16 - 16 + y^{2} =\]
\[= 2y^{2} - 8y.\]