#### Answer

$4x-y$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
(2\sqrt[]{x}+\sqrt{y})(2\sqrt[]{x}-\sqrt{y})
,$ 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\sqrt[]{x})^2-(\sqrt{y})^2
\\\\=
4x-y
.\end{array}