#### Answer

$y=-\dfrac{5}{2}$

#### Work Step by Step

We first use the distributive property to simplify. Then, using the properties of equality, we obtain that the value of the variable that satisfies the given equation, $
5(y-2)+2(y+1)=3(y-6)
,$ is
\begin{array}{l}\require{cancel}
5y-10+2y+2=3y-18
\\\\
5y+2y-3y=-18+10-2
\\\\
4y=-10
\\\\
y=-\dfrac{10}{4}
\\\\
y=-\dfrac{\cancel{2}\cdot5}{\cancel{2}\cdot2}
\\\\
y=-\dfrac{5}{2}
.\end{array}