#### Answer

$\frac{2y}{3x}$

#### Work Step by Step

Using the reciprocal rule to change the division sign to a multiplication sign and then canceling out similar factors, we obtain:
$\frac{4x}{5y}\div\frac{12x^{2}}{10y^{2}}$
=$\frac{4x}{5y}\times\frac{10y^{2}}{12x^{2}}$
=$\frac{1x}{5y}\times\frac{10y^{2}}{3x^{2}}$
=$\frac{1x}{1y}\times\frac{2y^{2}}{3x^{2}}$
=$\frac{1}{1}\times\frac{2y^{2-1}}{3x^{2-1}}$
=$\frac{1}{1}\times\frac{2y^{1}}{3x^{1}}$
=$\frac{2y}{3x}$