What should be subtracted from

Let $x$ be subtracted.

$\therefore\left(\frac{3}{4}-\frac{2}{3}\right)-x=\frac{-1}{6}$

$\Rightarrow\left(\frac{9}{12}-\frac{8}{12}\right)-x=\frac{-1}{6}$

$\Rightarrow\left(\frac{9-8}{12}\right)-x=\frac{-1}{6}$

$\Rightarrow x=\frac{1}{12}-\frac{-1}{6}$

$\Rightarrow x=\frac{1}{12}-\frac{-2}{12}$

$\Rightarrow x=\frac{1-(-2)}{12}$

$\Rightarrow x=\frac{1+2}{12}$

$\Rightarrow x=\frac{3}{12}$

$\Rightarrow x=\frac{1}{4}$