I'm off to bed but ...
You unfortunately have not really explained how your LEDs are connected - if you are using a circuit board, it sounds as if they are not able to be changed.
I think you are saying that each bar of 12 LEDs has four clusters, but you have not described just how these clusters are wired. Given three LEDs per cluster, are these three LEDs wired in series (voltage drop 5.4V, a regulated 5V supply would be insufficient)? So you presumably desire the four clusters in each bar to "ripple" in sequence along the bar.
If that is the case, what of the six bars? Should the pattern in each bar be identical or what?
Oh, you really will not need FETs, but if you can get logic level FETs, they would be fine. Ordinary dirt-cheap NPN general-purpose transistors will be entirely sufficient however. For each "channel", you need a resistor (4k7) to feed the base of the transistor from the Arduino, and a resistor in series with each LED cluster to control the LED current. The value of this resistor depends on how many LEDs in series and the supply voltage.