Divide $16\sqrt{ 75 }$  by $6\sqrt{ 12 }$  and select the option which represents the quotient.

Here, we have to divide $16\sqrt{ 75 }$  by $6\sqrt{ 12 }$ . 
So, we set up the division operation and simplify the expression as follows,
$\frac{16\sqrt{ 75 }}{6\sqrt{ 12 }}=\frac{8\sqrt{ 75 }}{3\sqrt{ 12 }}$ 
$\frac{8\sqrt{75}}{3\sqrt{12}}=\frac{8\sqrt{5\times 5\times 3}}{3\sqrt{3\times 2\times 2}}$
$=\frac{8}{3}\sqrt{\frac{5\times 5}{2\times 2}}$

$=\frac{8}{3}\times \frac{5}{2}$

$=\frac{20}{3}$
So, dividing $16\sqrt{ 75 }$  by $6\sqrt{ 12 }$ , the quotient is obtained as $\frac{20}{3}$ .
Hence, the correct option is $\frac{20}{3}$.