The seemingly correct resistor was so small so as to be useless for regulating current. For these LEDs, the current limiting resistor should have dropped no less than ~3V @20mA, so R= E/I = 3/0.02 = 150Ω.
That means you cannot run three 4V LEDs in series from 12V, and still have something left over for the resistor's voltage drop. You should reduce the string to only 2 LEDs in series per string, run the two strings in parallel, and use two strings, each with its own resistor.
I have never seen a LED with a forward drop of 4V. Can you post a link to its data sheet?
As to the second part of your question, I already answered it: Running LEDs without current regulation is like dancing on the head of a pin, or trying to balance a knife on its tip.