Question 632316
Equation of the line slope-intercept form
y=mx+b 
Given
Equation of the Given line
2x-3y=6
-3y=-2x+6
-3y/-3=(-2x+6)/-3
y=2x/3-2
y=(2/3)x-2
Compare with the equation of line slope-intercept form
Slope of the given = m = 2/3
Since lines are parallel their slope will be same 
Slope of the required line = m = 2/3
Point (0, 1)
We have a point and slope we can get easily the require line equation. 
Use Equation of the line point-slope form
m = y2-y1/x2-x1
Put the values in above equation, we have
2/3=(y-1)/(x-0)
2/3=(y-1)/x
2x=3(y-1)
2x=3y-3
-3y=-2x-3
-3y/-3=-(2x+3)/-3
y=2x/3+3/3
y=(2/3)x+1
Above equation is the equation of the required line

Graph
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y=(2/3)x-2 (Given line in green) 
y=(2/3)x+1 (Required line in Red)
{{{ graph(500,500,-10,10,-10,10,2x/3+1, 2x/3-2 ) }}}