I can think of two ways:
You are hit for 20, which knocks you to -11, you are level twelve, so you take 8 lethal and 12 non-lethal.
or
A 12th level barbarian is knocked to -1, they lose their rage hp’s (is it still two per level at that point) and drop to -25, 12 points of damage is converted to non-lethal, so they are instead at -13. At -13 most barbarians are likely to still be alive.
Which is most likely?
And with Paizo's hit -1 and lose your rage hp's is either version all that useful past level 11?