#### Answer

$a=-\dfrac{1}{2}$

#### Work Step by Step

Using properties of equality, the solution to the given equation, $
a-\dfrac{1}{6}=-\dfrac{2}{3}
$, is
\begin{array}{l}\require{cancel}
a-\dfrac{1}{6}+\dfrac{1}{6}=-\dfrac{2}{3}+\dfrac{1}{6}
\\\\
a=-\dfrac{4}{6}+\dfrac{1}{6}
\\\\
a=-\dfrac{3}{6}
\\\\
a=-\dfrac{\cancel{3}}{\cancel{3}\cdot2}
\\\\
a=-\dfrac{1}{2}
.\end{array}