[tex]\bf \dfrac{4}{3}\cdot \Big[ \dfrac{2}{3}-\Big( \dfrac{4}{5}-\Big(\dfrac{1}{2}-\dfrac{2}{3}\Big)\cdot\dfrac{2}{7}\Big)\cdot\dfrac{5}{14}\Big]=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \Big[ \dfrac{2}{3}-\Big( \dfrac{4}{5}-\dfrac{7}{6}\cdot\dfrac{2}{7}\Big)\cdot\dfrac{5}{14}\Big]=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \Big[ \dfrac{2}{3}-\Big( \dfrac{4}{5}-\dfrac{\not7}{\not6}\cdot\dfrac{\not2}{\not7}\Big)\cdot\dfrac{5}{14}\Big]=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \Big[ \dfrac{2}{3}-\Big( \dfrac{4}{5}-\dfrac{1}{3}\Big)\cdot\dfrac{5}{14}\Big]=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \Big[ \dfrac{2}{3}-\Big( \dfrac{4\cdot3}{5\cdot3}-\dfrac{1\cdot5}{3\cdot5}\Big)\cdot\dfrac{5}{14}\Big]=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \Big( \dfrac{2}{3}- \dfrac{12-5}{15}\cdot\dfrac{5}{14}\Big)=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \Big( \dfrac{2}{3}- \dfrac{7}{15}\cdot\dfrac{5}{14}\Big)=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \Big( \dfrac{2}{3}- \dfrac{\not7}{\not15}\cdot\dfrac{\not5}{\not14}\Big)=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \Big( \dfrac{2}{3}- \dfrac{1}{3}\cdot\dfrac{1}{2}\Big)=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \Big( \dfrac{2}{3}- \dfrac{1}{6}\Big)=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \Big( \dfrac{2\cdot2}{3\cdot2}- \dfrac{1}{6}\Big)=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \dfrac{4-1}{6}=[/tex]
[tex]\bf \dfrac{4}{3}\cdot \dfrac{3}{6}=[/tex]
[tex]\bf \dfrac{\not4}{\not3}\cdot \dfrac{\not3}{\not6}=[/tex]
[tex]\bf \dfrac{2}{1}\cdot \dfrac{1}{3}=[/tex]
[tex]\boxed{\bf \dfrac{2}{3}}[/tex]
