Lol that's quite a run on sentence, there.
A typical 7XXX 3-terminal regulator does a pretty damn good job.
What I was basically trying to say there is that the equation he mentioned works most of the time, but breaks down when you get towards the supply voltage. He will have to experiment with the resistance, which will be pretty low.
You don't even need 20mA of current through the LED, it can be lower and even somewhat higher. I still say you don't HAVE TO put a resistor, but you don't even need 20mA either, so a small one won't hurt the performance much.
Not having a resistor is only dangerous if the supply voltage might change. With three terminal regulators like the 7812 (+12V), the chances of deregulation are low. They build a decent amount of protection into those things. However, a human "oops" could burn out the LEDs since the dynamic resistance of the LED decreases fairly rapidly with forward voltage.
Assuming the V-I curve of his specific LEDs say that at 3V, the current is 20mA, then the resistance of the LED is 150ohms at that point.
12V / (4*150ohms) = 20mA as well, obviously.
Again, I agree, a small resistor won't hurt. Without any other information, i'd try around 50 ohms.