\(\frac{2}{3}\times\frac{1}{5}+\frac{3}{10}\times\frac{2}{3}+\frac{4}{6}\times\frac{1}{2}\)
\(=\frac{2}{3}\times\frac{1}{5}+\frac{3}{10}\times\frac{2}{3}+\frac{2}{3}\times\frac{1}{2}\)
\(=\frac{2}{3}\times\left(\frac{1}{5}+\frac{3}{10}+\frac{1}{2}\right)\)
\(=\frac{2}{3}\times\frac{10}{10}\)
\(=\frac{2}{3}\)