Answer
$\begin{align*}
\text{Slope: }&m=\dfrac{2}{3}
\\y-\text{intercept: }& 2
\end{align*}$
Work Step by Step
In the form $y=mx+b,$ the given equation, $
3y=6+2x
,$ is equivalent to
\begin{align*}
3y&=2x+6
\\\\
\dfrac{3y}{3}&=\dfrac{2x+6}{3}
\\\\
y&=\dfrac{2}{3}x+\dfrac{6}{3}
\\\\
y&=\dfrac{2}{3}x+2
.\end{align*}
The Slope-Intercept Form of the equation of lines, which is given by $y=mx+b,$ has slope $m$ and $y$-intercept of $b$. With the equation above then
\begin{align*}
\text{Slope: }&m=\dfrac{2}{3}
\\y-\text{intercept: }& 2
.\end{align*}
