#### Answer

$56+15\sqrt[]{2}$

#### Work Step by Step

Using $a(b+c)=ab+ac$, or the Distributive Property, and the properties of radicals, the given expression, $
(\sqrt[]{2}+6)(\sqrt[]{2}+9)
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[]{2}(\sqrt[]{2})+\sqrt[]{2}(9)+6(\sqrt[]{2})+6(9)
\\\\=
2+9\sqrt[]{2}+6\sqrt[]{2}+54
\\\\=
(2+54)+(9\sqrt[]{2}+6\sqrt[]{2})
\\\\=
56+15\sqrt[]{2}
.\end{array}