Answer
$p=\dfrac{5}{6}$
Work Step by Step
Using the properties of equality, the value of the variable that satisfies the given expression, $
-\dfrac{2}{3}+p=\dfrac{1}{6}
,$ is
\begin{array}{l}\require{cancel}
p=\dfrac{1}{6}+\dfrac{2}{3}
\\\\
p=\dfrac{1}{6}+\dfrac{4}{6}
\\\\
p=\dfrac{1+4}{6}
\\\\
p=\dfrac{5}{6}
.\end{array}