Question 67117
L has y-intercept (0, 2) and is perpendicular to the line with equation 2x -3y =6.
Perpendicular lines have slopes that are negative reciprocals of each other.  That means their slopes have opposite signs and are upside down.
If we put 2x-3y=6 into slope-intercept form: {{{highlight(y=mx+b)}}}, where m=slope and (0,b)=y-intercept, we can determine the slope we need.
{{{2x-3y=6}}}
{{{2x-2x-3y=-2x+6}}}
{{{-3y=-2x+6}}}
{{{-3y/-3=-2x/-3+6/-3}}}
{{{y=(2/3)x-2}}}  
This line has a slope of m=2/3 our line has a slope of m=-3/2
Using the slope intercept form: {{{highlight(y=mx+b)}}}
Our m=-3/2 and our (0,b)=(0,2)
{{{highlight(y=(-3/2)x+2)}}}
Let me know if you needed more than this.  I don't know what your instructions were.
Happy Calculating!!!!