Let the range of the function \( f(x)=6+16 \cos x \cdot \cos \left(\frac{\pi}{3}-x\right) \cdot \cos \left(\frac{\pi}{3}…

Let the range of the function

\(
f(x)=6+16 \cos x \cdot \cos \left(\frac{\pi}{3}-x\right) \cdot \cos \left(\frac{\pi}{3}+x\right)\)\(\sin 3 x \cdot \cos 6 x, x \in R\)

be \([\alpha, \beta]\). Then the distance of the point \((\alpha, \beta)\) from the line \(3 x+4 y+12=0\) is :

[JEE Main 2025, 23 Jan (Shift 2)]