Ответ:

[tex]\displaystyle\mathsf{-1\frac{2}{3} ;}[/tex]

[tex]\displaystyle\mathsf{\frac{a-2}{2} =\frac{b+3}{7} }\\\displaystyle\mathsf{7(a-2)=2(b+3)}\\\displaystyle\mathsf{7a-14=2b+6}\\\displaystyle\mathsf{7a=2b+20}\\\displaystyle\mathsf{a=\frac{2}{7}b+\frac{20}{7}. }\\\displaystyle\mathsf{\frac{b}{6} -\frac{7*(\frac{2}{7}b+\frac{20}{7})}{12} = \frac{b}{6}-\frac{2b+20}{12}= \frac{b}{6}-\frac{2(b+10)}{12}= \frac{b}{6}-\frac{b+10}{6}=\frac{b-b-10}{6}= }\\\displaystyle\mathsf{=-\frac{10}{6}=-\frac{5}{3}=-1\frac{2}{3} .}[/tex]