\(2\sqrt{6}+\sqrt{3}+4\sqrt{2}+3\)
\(=\left(\sqrt{2}+\sqrt{3}+\sqrt{6}\right)+\left(3\sqrt{2}+3+\sqrt{6}\right)\)
\(=\left(\sqrt{2}+\sqrt{3}+\sqrt{6}\right)+\left(\sqrt{18}+\sqrt{9}+\sqrt{6}\right)\)
\(=\left(\sqrt{2}+\sqrt{3}+\sqrt{6}\right)+\left(\sqrt{3.6}+\sqrt{3.3}+\sqrt{3.2}\right)\)
\(=\left(\sqrt{2}+\sqrt{3}+\sqrt{6}\right)+\sqrt{3}\left(\sqrt{2}+\sqrt{3}+\sqrt{6}\right)\)