$\left( -4x-2{y}^{2}+2y+2x \right)\div2$
Collect like terms$\left( -2x-2{y}^{2}+2y \right)\div2$
Write the division as a fraction$\frac{ -2x-2{y}^{2}+2y }{ 2 }$
Factor out $2$ from the expression$\frac{ 2\left( -x-{y}^{2}+y \right) }{ 2 }$
Cancel out the common factor $2$$-x-{y}^{2}+y$