\[7\sqrt{2} - 3\sqrt{8} + 4\sqrt{18} =\]
\[= 7\sqrt{2} - 3\sqrt{4 \cdot 2} + 4\sqrt{9 \cdot 2} =\]
\[= 7\sqrt{2} - 3 \cdot 2\sqrt{2} + 4 \cdot 3\sqrt{2} =\]
\[= 7\sqrt{2} - 6\sqrt{2} + 12\sqrt{2} = 13\sqrt{2}\]