Answer
$\color{blue}{6xyz^2\sqrt[3]{18y^2z^2}}$
Work Step by Step
Factor the radicand so that at least one factor is a perfect cube:
$=\sqrt[3]{216x^3y^3z^6(18y^2z^2)}
\\=\sqrt[3]{6^3x^3y^3(z^2)^3(18y^2z^2)}$
Bring out the cube root of the perfect cube factors to obtain:
$=\color{blue}{6xyz^2\sqrt[3]{18y^2z^2}}$