Answer
$-y\sqrt[3]{3x}$
Work Step by Step
Simplify each radicand to obtain
$\sqrt[3]{(8y^3)(3x)}-y\sqrt[3]{27(3x)}
\\=\sqrt[3]{(2y)^3(3x)}-y\sqrt[3]{3^3(3x)}
\\=2y\sqrt[3]{3x} - y\cdot 3\sqrt [3]{3x}
\\=2y\sqrt[3]{3x}-3y\sqrt[3]{3x}.$
RECALL:
The distributive property states that for any real numbers a, b, and c,
$ac + bc = (a+b)c
\\ac - bc = (a-b)c.$
Use the distributive to obtain
$(2y-3y)\sqrt[3]{3x}
\\=-y\sqrt[3]{3x}.$
