This is a frustrating feature of Adobe Audition: as far as I know, the manual never tells you step-by-step how to map the signal path. If I am wrong, someone tell me so I can pass the info along.
Go to Options/Device Properties/Wave Out and make sure your MOTU is recognized.
Also, check the channel I/O, shown in a small box to the left of the track in Multitrack View. it has buttons along the top edge for Record/Mute/Solo and In and Out fields. Right click on the In or Out to assign I/O to each track. The mixer I use has 8 I/O, so I can assign each of 8 tracks to its own output by right-clicking on the little window and ticking the option I want.
If you have enough channels on the MOTU for simultaneous playback (I assume you are using the MOTU PCI interface, not a stereo sound card, right?) you can assign 8 playback tracks (for example) as 1L, 1R, 2L, 2R, 3L, 3R, 4L and 4R. I use a 16-channel mixer in my setup, where channels 1-8 are input ("record" to the computer) and mixer channels 9-16 are output ("playback" to the computer): track 1 goes into channel 9 (panned hard left), 2 > 10 (panned hard right), 3 > 11 (left), 4 > 12 (right), 5 > 13 (left), 6 > 14 (right), 7 > 15 (left) and 8 > 16 (right). This puts each track on its own fader. How to route that signal once it gets back out of the computer depends on your hardware. My setup allows 3 separate paths (monitor speakers, headphone amp, or room playback).