\(\left(3\frac{1}{2}+5\frac{2}{3}\right)\times\frac{8}{19}-\left(2\frac{1}{2}+4\frac{2}{3}\right)\times\frac{8}{19}\)
\(=\frac{8}{19}\times\left[\left(3\frac{1}{2}+5\frac{2}{3}\right)-\left(2\frac{1}{2}+4\frac{2}{3}\right)\right]\)
\(=\frac{8}{19}\times\left(3\frac{1}{2}+5\frac{2}{3}-2\frac{1}{2}-4\frac{2}{3}\right)\)
\(=\frac{8}{19}\times\left[\left(3\frac{1}{2}-2\frac{1}{2}\right)+\left(5\frac{2}{3}-4\frac{2}{3}\right)\right]\)
\(=\frac{8}{19}\times\left(1+1\right)\)
\(=\frac{8}{19}\times2=\frac{16}{19}\)