Mikey,
The short answer is: it depends a whole lot on your mixer and on how you record, as in: whether you are a 'one-track at a time' home recordist, or you work at home with a band and you or someone else can mix while the playing goes on.
In the latter scenario, if you can hook every live signal through the mixer, and your mixer does indeed have an "8-out" function, then you can downmix your sources live from however many inputs you have on the mixer and now have 8 'stems' on the Tascam, that is, 8 tracks of semi-mixed channels from the larger number coming in.
Then you can return the 8 tape tracks into the mixer (again, depending on mixer) and do your final downmix from the 8 tracks down to a 2-track analog or digital master recorder or you can send the 8 'stem tracks' into a PC for final mixing.
If you are doing 'one track at a time', your choices are that you can input any line-level source (direct box, mixer input, separate pre-amp) one or two at a time onto the 8 tracks of the Tascam directly (if you like what you hear this way.)
Then your mixer becomes the end receiver of your 8 tape tracks and you can fiddle as much as you want before making a 2-track master or sending the 8 tracks into a PC for further manipulation.
These are just two basic scenarios, mind you, but they are pretty common so they should give you some ideas.
Best,
C.