Answer
The answer is $4x^2 - 4x + 6 - \frac{11}{2x + 3}$.
Work Step by Step
Now, the dividend $4x^2 + 7 + 8x^3$ can be rewritten as $8x^3 + 4x^2 + 0x + 7$.
$\space \space \space \space \space \space \space \space \space \space \space \space \space \space4x^2 - 4x + 6$
$2x + 3 /\overline{8x^3 + 4x^2 + 0x + 7}$
$\space \space \space \space \space \space \space \space \space \space \space \space \space \space \underline{8x^3 +12x^2}$
$\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space -8x^2 + 0x$
$\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \underline{-8x^2 -12x}$
$\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space 12x + 7$
$\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \underline{12x + 18}$
$\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space -11$
The answer is $4x^2 - 4x + 6 - \frac{11}{2x + 3}$.