We find the $x$-intercept by setting $y = 0.$ Then $3x = 12 + 2x,$ so $x = 6.$
We find the $y$-intercept by setting $x = 0.$ Then $-6y = 12,$ so $y = -2.$
The distance between $(6,0)$ and $(0,-2)$ is $\sqrt{(6 - 0)^2 + (0 - (-2))^2} = \boxed{2 \sqrt{10}}.$
Find the distance between the $x$-intercept and the $y$-intercept of the graph of the equation $3x - 6y = 12 + 2x - 4y$.
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