3d Geometry

If \(\mathrm{d}_1\) is the shortest distance between the lines \(x+1=2 y=-12 z, x=y+2=6 z-6\) and \(\mathrm{d}_2\) is the shortest distance between the lines \(\frac{x-1}{2}=\frac{y+8}{-7}=\frac{z-4}{5}, \frac{x-1}{2}=\frac{y-2}{1}=\frac{z-6}{-3}\), then the value of \(\frac{32 \sqrt{3} \mathrm{~d}_1}{\mathrm{~d}_2}\) is :