Answer
$2y^{2}+3y-1$
Work Step by Step
$\begin{array}{ccccccccccc}
& & 2y^{2} & +3y &-1 & \\
& &--&-- &--& \\
2y+3&) & 4y^{3} & +12y^{2} & +7y& -3 & & \\
& & 4y^{3} & +6y^{2} & & & \color{red}{\leftarrow \small{2y^{2}(2y+3) } } \\
& &--&-- & & & \color{red}{ \small{subtract}} \\
& & & 6y^{2} & +7y& -3 & \\
& & & 6y^{2} & +9y& & \color{red}{\leftarrow \small{3y(2y+3) } }\\
& & &--&-- & &\color{red}{ \small{subtract}} \\
& & & & -2y & -3 & \\
& & & & -2y & -3 & \color{red}{\leftarrow \small{(-1)(2y+3) } }\\
& & & &-- & -- &\color{red}{ \small{subtract}} \\
& & & & & 0 &
\end{array}$
Quotient = $2y^{2}+3y-1$
Remainder = $ 0$.
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{ 4y^{3}+12y^{2}+7y-3}{2y+3}$ = $2y^{2}+3y-1$
