Mathematics Question from JEE Main 2024 · 30 January, Shift 1

If $d_1$ is the shortest distance between the lines $x + 1 = 2y = -12z$ and $x = y + 2 = 6z - 6$, and $d_2$ is the shortest distance between the lines $\frac{x-1}{2} = \frac{y+8}{-7} = \frac{z-4}{5}$ and $\frac{x-1}{2} = \frac{y-2}{1} = \frac{z-6}{-3}$, then the value of $\frac{32\sqrt{3}\,d_1}{d_2}$ is _____.