#### Answer

$40|xy|\sqrt{3}$

#### Work Step by Step

RECALL:
$\sqrt{a} \cdot \sqrt{b} = \sqrt{a\cdot b}, a\gt0, b\gt 0.$
Use the rule above to have
$20\sqrt{(2x)(6xy^2)}
\\=20\sqrt{12x^2y^2}
\\=20\sqrt{4x^2y^2(3)}
\\=20\sqrt{(2xy)^2(3)}
\\=20(2)|xy|\sqrt{3}
\\=40|xy|\sqrt{3}.$