Let $$A, B$$ and $$C$$ be three points on the parabola $$y^2 = 6x$$ and let the line segment $$AB$$ meet the line $$L$$ through $$C$$ parallel to the $$x$$-axis at the point $$D$$. Let $$M$$ and $$N$$ respectively be the feet of the perpendiculars from $$A$$ and $$B$$ on $$L$$. Then $$\left(\frac{AM \cdot BN}{CD}\right)^2$$ is equal to ________