Answer
$6y^4-8y^3+14y^2$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $
2y^2(3y^2-4y+7)
,$ is equivalent to
\begin{array}{l}\require{cancel}
2y^2(3y^2)+2y^2(-4y)+2y^2(7)
\\\\=
6y^4-8y^3+14y^2
.\end{array}