$a)$

$w\left(x\right)=2\left(x^5+\frac{1}{2}{x}^2+3\right)-3\left(-2x^4+\frac{x^2}{3}+2\right)=$

$=2x^5+x^2+6+6x^4-x^2-6=$

$=2x^5+6x^4$

$st\left(w\right)=5$

$sum{a}_w=2+6=8$