Answer
The $y$-intercept is $-2$.
The slope is $\frac{2}{3}$.
See the graph below.
Work Step by Step
First, we have to get the equation's slope-intercept form, that is $y=mx+b$:
Isolate $y$ to obtain:
\begin{align*}
2x-3y+3y&=6+3y\\
2x&=3y+6\\
2x-6&=3y+6-6\\
2x-6&=3y\\
\frac{2x-6}{3}&=\frac{3y}{3}\\
\frac{2}{3}x-2&=y\\
y&=\dfrac{2}{3}x-2
\end{align*}
This form of the equation is the slope-intercept form.
In this form, the slope of the line equals to the coefficient of $x$ (which is $m$) and the $y$-intercept equals to the constant $b$.
Therefore in the equation $y=\frac{2}{3}x-2$:
The $y$-intercept is $-2$.
The slope is $\frac{2}{3}$.
In order to graph the line, we have to sketch the $y$-intercept, that is $(0,-2)$.
As the slope is $\frac{2}{3}$, we can find another point that we can also sketch.
The slope is the change in $y$ for every $1$ unit change of $x$.
Thus, a slope of $\frac{2}{3}$ means a $1$-unit increase in $x$ will result to a $\frac{2}{3}$-unit increase in $y$. This is equivalent to a $2$-unit increase in $y$ for a $3$-unit increase in $x$.
Using $(0,-2)$ as the starting point and a slope of $\frac{2}{3}$, the coordinates of another point on the line would be:
$(0+3, -2+2)=(3, 0)$
Plot the two points then connect them using a straigiht line.
Refer to the graph above,
