\[(y - 3)(5 - y) - (4 - y)(y + 6) =\]
\[= 5y - y^{2} - 15 + 3y - \left( 4y + 24 - y^{2} - 6y \right) =\]
\[= 8y - y^{2} - 15 - 4y - 24 + y^{2} + 6y =\]
\[= 10y - 39.\]