High Power RGB Led control
Just poke around with a 30V power supply with a 1K resistor in series, as Starblue suggests and you'll quickly figure it out (I suggest the resistor because the output capacitor of even a current-limited power supply could damage the LEDs conceivably) 

Probably 3 strings of series or series/parallel with a common. Whether it's common anode or cathode is unknown.

Chances are the top strip in your photo is the common, and the bottom left is red and the other two are green and blue (maybe not that order for green and blue).  







simulate this circuit &ndash; Schematic created using CircuitLab

You need to limit the operating current into the LEDs to less than the smaller of the rated current and the maximum allowed by the power dissipation. As in the comments if you power this up at anywhere near the claimed 20W input power it will see perhaps 18W of heating and will expire in short order.