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Use a potentiometer to measure the (forward) resistance across the strip. Call this resistance R1. The series resistor for one should have a resistance of R2=R1*(14-12)/12 = R1/6. Make sure you use a resistor that can handle the current you'll be drawing, calculated as I=V/R=14/(R1+R2).
To run all four strips on a single resistor, do the same as above, but your value for R1 will be all of the LED strips in parallel. Since they're all (presumably) the same resistance, you can just divide by 4 to get this number for 4 strips. Again, check to make sure the resistor you get can handle the amps you need.
Hope this helps. Good luck!
Also, regarding whether it might be a heat issue, it is possible but not likely. I have some 20W LEDs that I'm modding for headlamps, and they will get hot enough to fail without a proper heatsink, but they have to get REALLY hot for that to happen I think (haven't broken one yet, but I have burned myself a little). The failure you're talking about seems more like an excessive voltage failure. I think if it overheated externally, you would see damage on the plastic before the LEDs themselves would give out.
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