A 24W rated supply should be fine for a 12W load, even allowing for a little loss in the converter.If I use a12v 2a dc power supply would that be sufficient to power the circuit of a Joule thief? According to my calculations the 120 leds are drawing a total of 12w, so a 12v 2a output should easily cover it. I just thought that the Joule thief would be more economical.
Chances are you don't need a Joule thief per se if you use a 12V supply. A Joule thief is for producing spikes in voltage to flash an LED (faster than you can see) when the power supply would not otherwise be able to light the LED. So a 3.5V LED can run off a single AA battery, for instance.
In your case, you need to match up your power supply to whatever the LEDs need to operate. That's a job for a DC-DC converter. Buck to reduce voltage (12V to 6V), boost to increase voltage. Combined buck/boost to allow for a wide range of input and outputs. Aa Joule thief is a type of boost converter but usually limited to small loads like a single LED.