Find the following products and express answers in simplest radical form. All va

Given expression:
$3\sqrt[3]{4}(2\sqrt[3]{2}-6\sqrt[3]{4})$
$3\sqrt[3]{4}(2\sqrt[3]{2}-6\sqrt[3]{4})=3\sqrt[3]{4}(2\sqrt[3]{2}-3\sqrt[3]{4})(6\sqrt[3]{4})$
$6\sqrt[3]{4}\sqrt[3]{2}-18\sqrt[3]{4}\sqrt[3]{4}$
$=6\sqrt[3]{4\times 2}-18\sqrt[3]{4\times 4}$
$6\sqrt[3]{8}-18\sqrt[3]{16}$
${\displaystyle =6{\left(8\right)}^{\frac{1}{3}}-18{\left(16\right)}^{\frac{1}{3}}}$
${\displaystyle 6{(2\times 2\times 2)}^{\frac{1}{3}}-18{(2\times 2\times 2)}^{\frac{1}{3}}}$
${\displaystyle =6\left(2\right)-18\left(2\right){\left(2\right)}^{\frac{1}{3}}}$
${\displaystyle =12-36{\left(2\right)}^{\frac{1}{3}}}$
${\displaystyle =12-36{\left(2\right)}^{\frac{1}{3}}}$
${\displaystyle =12-36\sqrt[3]{2}}$
Hence
$3\sqrt[3]{4}(2\sqrt[3]{2}-6\sqrt[3]{4})=12-36\sqrt[3]{2}$