#### Answer

$\color{blue}{y=-\frac{2}{3}x}$
Refer to the graph below.

#### Work Step by Step

RECALL:
(1) Parallel lines have the same slope.
(2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the y-intercept.
The line is parallel to $2x+3y=6$.
Write this equation in slope-intercept form to find its slope.
$2x+3y=6
\\3y=6-2x
\\3y=-2x+6
\\\frac{3y}{3}=\frac{-2x+6}{3}
\\y=-\frac{2}{3}x+2$
The line has a slope of $-\frac{2}{3}$.
This means that the slope of the line parallel to it is also $-\frac{2}{3}$.
Thus, the tentative equation of the line we are looking for is $y=-\frac{2}{3}$.
To find the value of $b$, substitute the x and y values of the point $(-3, 2)$ to obtain:
$y=-\frac{2}{3}x+b
\\2=-\frac{2}{3}(-3)+b
\\2=2+b
\\2-2=b
\\0=b$
Thus, the equation of the line is:
$y=-\frac{2}{3}x+0
\\\color{blue}{y=-\frac{2}{3}x}$
Refer to the graph in the answer part above.