[tex]4\sqrt[3]{2}:6\sqrt[3]{4} = \frac{4\sqrt[3]{2}}{6\sqrt[3]{4} } =\frac{2}{3}\cdot \sqrt[3]{\frac{2}{4}} =\frac{2}{3}\cdot \sqrt[3]{\frac{1}{2}} =\frac{2}{3}\cdot \frac{\sqrt[3]{1}}{\sqrt[3]{2}}=\frac{2}{3}\cdot \frac{\sqrt[3]{1}}{\sqrt[3]{2}}\cdot \frac{\sqrt[3]{4}}{\sqrt[3]{4}}=\\\\=\frac{2\sqrt[3]{4}}{3\sqrt[3]{2*4}}=\frac{2\sqrt[3]{4}}{3\sqrt[3]{8}}=\frac{2\sqrt[3]{4}}{3 \cdot 2}=\frac{\sqrt[3]{4}}{3}[/tex]