Connect the red end of the RCA cable to to boombox's "Right Output" RCA jack. The Right Output jack is labeled in red, and is located on the side or back of the device, depending on model.
Connect the white end of the RCA cable to the "Left Output" RCA jack of the boombox. The Left Output jack will be white in color as well.
Plug the other ends of the cable into your powered subwoofer. Plug the red end of the cable into the "Right Input" jack on the back of the subwoofer, then the white end of the cable into the "Left Input" RCA jack.
Power on your boombox and subwoofer. Set your subwoofer's volume to its middle position, then slowly increase the output level on the boombox until you have reached the desired level.