The SRS (Standard Roleplaying System) by FarEast Amusement Research uses 2d6 roll over for its dice mechanic.
You roll your two dice, add modifiers, and compare the total to a difficulty value. If you roll equal to the difficulty value or higher, the action is successful.
Difficulty values are:
6~8 for an easy action
9~11 for a doable action
12~15 for a hard action
16+ for a nearly impossible action

Now, let's say that you wanted to convert the mechanic to 2d12 for increased granularity for to downplay dice modifiers.
What would be the best way to convert the difficulty values?
Chances of success you remain more or less the same. About 72% minimum for easy actions, 27% for doable actions, 2.8% for hard actions
Values should still convert quickly and easily back to the normal SRS values for purposes of compatibility with other games from that system

I've been doing my own math and comparing numbers via Roll20.
http://anydice.com/program/942c
I have never been good at math, but if I am comparing these numbers correctly, then...
A roll of 6 on 2d6 is about equivalent to a roll of 11 on 2d12
7 is equivalent to 13
8 is equivalent to 15
9 is equivalent to 17
10 is equivalent to 19
11 is equivalent to 21
12 is equivalent to 23

Probabilities don't have to match of perfectly as long as the conversion is close enough to do the job.
So I could just double difficulty values from SRS to determine equivalent difficulty values for this 2d12 version, and mash things down to fit, correct?
11~16 for an easy action
17~22 for a doable action
23~30 for a hard action
31+ for a nearly impossible action

How does that look?

Here's a table of the various probabilities. You won't get an exact equivalent for the range bands and will need to make a judgement call on where to separate.

EDIT: Well that was illegible. Sorry. I don't know how to paste and get columns to work in the forum software. I'll have to futz around to get a readable version.

OK as an interim measure I posted the tables of probabilities on my blog.

Thank you kindly!

Nice blog, by the way. I think I'll start following that.
*Favorites star clicked*