$6\sqrt{\dfrac{8}{9}}-5\sqrt{\dfrac{32}{25}}+14\sqrt{\dfrac{18}{49}}$
$=6\sqrt{\dfrac{2^3}{3^2}}-5\sqrt{\dfrac{2^5}{5^2}}+14\sqrt{\dfrac{3^2.2}{7^2}}$
$=6.\dfrac{2}{3}\sqrt{2}-5.\dfrac{4}{5}\sqrt{2}+14.\dfrac{3}{7}\sqrt{2}$
$=4\sqrt{2}-4\sqrt{2}+6\sqrt{2}$
$=6\sqrt{2}$