\[\left( 3\sqrt{2} + \sqrt{18} \right) \cdot \sqrt{2} =\]
\[= 3\sqrt{2} \cdot \sqrt{2} + \sqrt{9 \cdot 2} \cdot \sqrt{2} =\]
\[= 3 \cdot 2 + 3 \cdot 2 = 6 + 6 = 12.\]