\begin{align*} A &= \frac 5 6 - \frac 1 6 \times 7 + \frac 4 9& \\ &=\frac 5 6 - \frac 7 6 + \frac 4 9& \\ &=\frac{15-21+8}{28}& \\ &=\frac 2 {18}& \\ &=\boxed{\frac 1 9.}& \\ B &= \left(2 - \frac 1 3\right):\frac{20}9& \\ &=\frac{6-1}3 \times \frac 9 {20}& \\ &=\frac{5}{3}\times \frac{9}{20}& \\ &=\frac{\overset{1}{\cancel{5}}\times\overset{3}{\cancel{9}}}{\underset{1}{\cancel{3}}\times\underset{4}{\cancel{20}}}& \\ &=\boxed{\frac 3 4.}& \\ C &= \frac 4 3 + \frac 1 2 : \left(\frac{-3} 4 + \frac 1 6\right)& \\ &= \frac 4 3 + \frac 1 2 : \frac{-9+2}{12}& \\ &=\frac 4 3 + \frac 1 2 \times \frac{-7}{12}& \\ &=\frac 4 3 - \frac 1 2 \times \frac{12} 7& \\ &=\frac 4 3 - \frac 6 7& \\ &=\frac{28-18}{21}& \\ &=\boxed{\frac{10}{21}.}& \\ D &= \frac 3 8 - \frac 3 {14} \times \frac 7 6& \\ &=\frac 3 8 - \frac{\overset{1}{\cancel{3}}\times\overset{1}{\cancel 7}}{\underset{2}{\cancel{14}}\times\underset{2}{\cancel 6}}& \\ &=\frac 3 8 - \frac 1 4& \\ &= \frac {3-2} 8& \\ &=\boxed{\frac 1 8.}& \end{align*}