\(=\sqrt[3]{2\sqrt{3}+4\sqrt{2}}\sqrt[6]{\left(4\sqrt{2}\right)^2+2.4\sqrt{2}.2\sqrt{3}+\left(2\sqrt{3}\right)^2}\)

\(=\sqrt[3]{2\sqrt{3}+4\sqrt{2}}\sqrt[6]{\left(2\sqrt{3}+4\sqrt{2}\right)^2}\)

\(=\sqrt[3]{2\sqrt{3}+4\sqrt{2}}\sqrt[3]{2\sqrt{3}+4\sqrt{2}}\)

\(=\sqrt[3]{\left(2\sqrt{3}+4\sqrt{2}\right)^2}\)

\(=\sqrt[3]{44+16\sqrt{6}}\)