Question 1
[tex]0.1x=0.2(x+2)\\\\0.1x=0.2x+0.4\\\\-0.1x=0.4\\\\x=\boxed{-4}[/tex]
Question 2
[tex]\frac{1}{6}d+\frac{2}{3}=\frac{1}{4}(d-2)[/tex]
Multiplying both sides by 12,
[tex]2d+8=3(d-2)\\\\2d+8=3d-6\\\\8=d-6\\\\d=\boxed{14}[/tex]