I would not refer the user to videos with a running time of over 1 hour to clarify a question. You are putting him to a hard test of patience. For a 1st overview of TM FX you should better point to the short videos which cover all parts of TM FX quickly but detailed enough.

The answer is quite simple. Audio from the operating system and all applications is first placed in the middle row of TM FX (assuming "full mode", TM FX default operation mode). You are setting this in every application.
Then TM FX acts like a patch bay, you have to route audio from there to each of the HW outputs individually.
This brings the wonderful flexibility to decide WHAT exactly you want to hear on EACH of the HW outputs of your recording interface (from hw inputs with near-zero latency and/or from sw playback from the pc via USB/... with the usual round trip latency).

My recommendation: it's best to divide the audio streams cleverly at this point.

For example:
AN 1/2: Sound output from the Windows operating system (don't forget to set up the WDM device for this and make it the default sound device in the Windows sound settings).
AN 3/4: Sound output from audio players with ASIO support, e.g. MusicBee
AN 5/6: Sound output of games (if the audio channel is selectable in games, set up a WDM device for this as well)
AN 7/8: Sound output from the main stereo bus of your DAW.
AS1/2: Maybe a submix of your DAW or part of DRUM section separately ? You decide.
ADAT 3/4: Maybe another submix of your DAW or anothe part of DAW project separately ? You decide.

Once this is done, you are ready to see audio from these different areas of your computer in TM FX in the middle row (sw playbacks).

Now comes the routing task in TM FX, deciding what you want to hear on your actual HW outputs (Bottom Row) and at what volume level. This can be any mix of audio streams from
- HW inputs (top row) and
- SW playbacks (bottom row)
for each of the HW outputs individually. Every HW output is also being referred to be a "submix", as you are creating a "submix" for each of the outputs. Hence the name "submix mode", you click to an HW output and create the submix by moving the HW input and SW playback faders (top/middle row) as you need.

First something basic. The outputs of the main monitors and headphones (for example, AN1/2 and AN3/4) should be assigned to the TM FX Control Room, so that you can also use the usual control room features offered by TM FX, e.g. mono, DIM, ... when working/monitoring using these outputs.

That's what the "Assign" button in TM FX is for (on the right hand side in the control room)
Before routing, you should quickly assign the outputs in a meaningful way:
Assign -> AN1/2 -> Main Out
Assign -> AN3/4 -> Phones1

After that basic setup which should be done 1st IMHO (see also my step by step setup guide, links at the end) you can go to the actual routing part in submix mode (check on the right if the mode is active).

Now click on "Main", that is HW Output 1/2, which is now in the Control Room at the bottom right after the assign.
Now select which channels you want to listen to for this output.
So pull up the faders from the middle row (SW Playbacks) as you need them.
SW Playback AN1/2 - Windows Sound
SW Playback AN3/4 - MusicBee player
SW Playback AN5/6 - Games
SW Playback AN7/8 - DAW
usually to 0dB, but you can even create a very special submix to play a game, listen to a youtube letsplay video and using your audio player to get your beloved background music ... I can tell you .. this is the way to go, the flexibility you ever wanted. If not exactly that, then something similar .. most important .. you CAN do .. it's no must.

Everything you don't want to hear from HW inputs and SW playbacks, pull the faders all the way down to infinity.

After you have gained this basic understanding of operation, then everything is clear and you should be able to answer the question yourself ....

Audio output is done on the channel in the middle row, as you have set it in the respective application.
And the TM FX routing for each individual output decides which submix of HW inputs and SW playbacks you hear on this channel.

Here a step by step primer that I wrote how to setup TM FX for a good basic setup:
https://www.tonstudio-forum.de/blog/ind … rnal-equi/

Here a complete list of TM FX videos:
https://www.tonstudio-forum.de/blog/ind … al-Videos/

The manual is also a very good source of information, it covers everything to the point and is nicely structured:
BBF Pro DE: https://www.rme-audio.de/downloads/bface_pro_d.pdf
BBF Pro EN: https://www.rme-audio.de/downloads/bface_pro_e.pdf