The given equation of the line is
[tex]\begin{gathered} 2x-3y=6 \\ 3y=2x-6 \\ y=\frac{2}{3}x-2 \end{gathered}[/tex]Hence slope of the line is
[tex]\frac{2}{3}[/tex]Since the line passing through (0,1) parallel to the given line then slope is same for both of them
Since (0,1) is a point so the intercept is c=1
So the equation is
[tex]\begin{gathered} y=mx+c \\ y=\frac{2}{3}x+1 \end{gathered}[/tex]