\[(y + 2)(y + 3) - y(y - 1) =\]
\[= y^{2} + 3y + 2y + 6 - \left( y^{2} - y \right) =\]
\[= y^{2} + 5y + 6 - y^{2} + y =\]
\[= 6y + 6.\]