OK, we'll assume that you're talking about the Digidesign (now Avid) Mbox 2 and a traditional mixing console. The principles involved apply in general to any of the Mbox range (except the Mini, which doesn't have audio inputs) and indeed to any small audio interface from any manufacturer.
In any recording system there are a certain number of inputs, a number of tracks that can be recorded, and a number of outputs.
In traditional recording with mixing consoles and hardware multitrack recorders, the multitrack recorder always has the same number of inputs, tracks and outputs. So a 24-track recorder has 24 inputs, 24 tracks and 24 outputs.
But it isn't like this in DAW recording.
The Mbox 2 has only two inputs and two outputs*. The Pro Tools LE software that it connects to is capable of up to 96 channels of audio in 48 mono or stereo tracks. But there are only two channels in, and two channels out, of the system.
*The Mbox 2 has two digital inputs too, but you would need digital sources or additional A-D converters to use them.
This isn't a problem for home recordists who only ever record one instrument or vocal at a time.
But the tiny number of inputs and outputs, compared to the immense number of recordable tracks, imposes limitations on how the system can be used with a conventional mixing console.
Well you can mix all the mics into stereo and record them through your Mbox onto a stereo track. That's fine - you have a recording.
It would be possible, say, to record the basic instruments into stereo, then overdub vocals and solos one-by-one. This might be a workable compromise.
You would however long to have an audio interface with more inputs. In fact you really need to have as many inputs as the number of tracks you want to record simultaneously.
Currently if you want to keep your costs down, you will have to look outside of the Pro Tools LE range, and use a different DAW software as Pro Tools LE only works with Digidesign (Avid) interfaces. Pro Tools HD systems, with more inputs and outputs, are fiendishly expensive.
Now let's consider mixing...
The answer once again is unfortunately no - since you only have two outputs, you can't mix using your console. You would have to mix inside the DAW software.
In summary therefore, there isn't really much point using a mixing console with a small audio interface. The only workable scenario is where you want to mix live as the band plays, and record into your DAW in stereo.
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