Answer
$6\sqrt[4]{63}+4\sqrt[4]{35}-3\sqrt[4]{54}-2\sqrt[4]{30}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$, or the product of 2 binomials, and the properties of radicals, the given expression, $
(2\sqrt[4]{7}-\sqrt[4]{6})(3\sqrt[4]{9}+2\sqrt[4]{5})
,$ is equivalent to
\begin{array}{l}\require{cancel}
(2\sqrt[4]{7})(3\sqrt[4]{9})+(2\sqrt[4]{7})(2\sqrt[4]{5})-(\sqrt[4]{6})(3\sqrt[4]{9})-(\sqrt[4]{6})(2\sqrt[4]{5})
\\\\=
2(3)\sqrt[4]{7(9)}+2(2)\sqrt[4]{7(5)}-3\sqrt[4]{6(9)}-2\sqrt[4]{6(5)}
\\\\=
6\sqrt[4]{63}+4\sqrt[4]{35}-3\sqrt[4]{54}-2\sqrt[4]{30}
.\end{array}
