jmc

By subtracting $3x$ and dividing both sides by $-2$ we get $y=\frac{3}{2}x-3$ meaning this line has slope $\frac{3}{2}$ and any line perpendicular to it has slope $-\frac{2}{3}$. Using the slope-intercept form of a line we get that the equation of the line perpendicular to it with $y$-intercept of 2 is $y=-\frac{2}{3}x+2$. We find the $x$-intercept by letting $y=0$ which gives $x=\boxed{3}$.