If the thickness of a pile of 12 cardboards is 65 mm,

Let x mm be the required thickness. Then, we have:

Clearly, when the number of cardboard is more, the thickness will also be more.

So, it is a case of direct proportion.

Now, $\frac{65}{12}=\frac{x}{312}$

$\Rightarrow x=\frac{65 \times 312}{12}$

$\Rightarrow x=1690$

Therefore, the thickness of the pile of 312 cardboards is 1690 mm.