a)

$\begin{array}{l}x+\left(-\frac{2}{9}\right)=\frac{-7}{12}\\ x=\frac{-7}{12}+\frac{2}{9}\\ x=\frac{-21}{36}+\frac{8}{36}\\ x=\frac{-13}{26}\end{array}$

Vậy $x=\frac{-13}{26}$.

b)

$\begin{array}{l}(-0,1)-x=\frac{-7}{6}\\ \frac{-1}{10}-x=\frac{-7}{6}\\ x=\frac{-1}{10}+\frac{7}{6}\\ x=\frac{-3}{30}+\frac{35}{30}\\ x=\frac{32}{30}\\ x=\frac{16}{15}\end{array}$

Vậy $x=\frac{16}{15}$

c)

$\begin{array}{l}(-0,12)\cdot \left(x-\frac{9}{10}\right)=-1,2\\ \frac{-3}{25}\cdot \left(x-\frac{9}{10}\right)=\frac{-6}{5}\\ x-\frac{9}{10}=\frac{-6}{5}:\left(\frac{-3}{25}\right)\\ x-\frac{9}{10}=\frac{-6}{5}.\frac{-25}{3}\\ x-\frac{9}{10}=10\\ x=10+\frac{9}{10}\\ x=\frac{109}{10}\end{array}$

Vậy $x=\frac{109}{10}$.

d)

 $\begin{array}{l}\left(x-\frac{3}{5}\right):\frac{-1}{3}=0,4\\ \left(x-\frac{3}{5}\right):\frac{-1}{3}=\frac{2}{5}\\ x-\frac{3}{5}=\frac{2}{5}.\frac{-1}{3}\\ x-\frac{3}{5}=\frac{-2}{15}\\ x=\frac{-2}{15}+\frac{3}{5}\\ x=\frac{7}{15}\end{array}$

Vậy $x=\frac{7}{15}$.