#### Answer

$\dfrac{8x^{2}}{y^{3}}\div\dfrac{4x^{2}y^{3}}{6}=\dfrac{12}{y^{6}}$

#### Work Step by Step

$\dfrac{8x^{2}}{y^{3}}\div\dfrac{4x^{2}y^{3}}{6}$
Divide the two rational expressions:
$\dfrac{8x^{2}}{y^{3}}\div\dfrac{4x^{2}y^{3}}{6}=\dfrac{(8x^{2})(6)}{(4x^{2}y^{3})(y^{3})}=\dfrac{48x^{2}}{4x^{2}y^{6}}=...$
Simplify by removing repeated factors in the numerator and the denominator:
$...=\dfrac{48}{4y^{6}}=\dfrac{12}{y^{6}}$