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