The value of $$\frac{1}{3}+\frac{6}{7}\div\frac{6}{3}+\frac{8}{9}-\frac{2}{3}\times\frac{4}{3}$$ is:
$$\dfrac{1}{3}+\dfrac{6}{7}\div\dfrac{6}{3}+\dfrac{8}{9}-\dfrac{2}{3}\times\dfrac{4}{3} $$
$$= \dfrac{1}{3} + \dfrac{6}{7}\times\dfrac{3}{6}+\dfrac{8}{9}-\dfrac{8}{9}$$
$$= \dfrac{1}{3} + \dfrac{3}{7} = \dfrac{7+9}{21}$$
$$= \dfrac{16}{21}$$
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