Chapter 8 - Section 8.2 - Multiplying and Dividing Radicals - Exercise Set - Page 585: 102

$2\sqrt[3]{6}$

Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $ \sqrt[3]{12}\cdot\sqrt[3]{4} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{12(4)} \\\\= \sqrt[3]{48} \\\\= \sqrt[3]{8\cdot6} \\\\= \sqrt[3]{(2)^3\cdot6} \\\\= 2\sqrt[3]{6} .\end{array}