#### Answer

$4-\sqrt[3]{36}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
(2+\sqrt[3]{6})(2-\sqrt[3]{6})
,$ use the special product on multiplying the sum and difference of like terms.
$\bf{\text{Solution Details:}}$
Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
(2)^2-(\sqrt[3]{6})^2
\\\\=
4-\sqrt[3]{6^2}
\\\\=
4-\sqrt[3]{36}
.\end{array}