Think of a channel as a complete pathway. It "channels" the sound from an input source to a final destination. A 4-channel mixer, such as the Sound Devices 442, can take 4 individual inputs and rout them to seveal different outputs. It has a stereo mix out, but it also has a direct output for each channel which allows each channel to be sent out separately to a multi-track recorder.
"Track" is a leftover term from tape days, when studio recordings went to magnetic tape and the tape had a certain number of record tracks on it. Each track took up a physical space on the tape, the width of which was determined by the width of the overall tape and the total number of tracks occupying the tape. For instance, a 1/4" 8-track tape recorder ran a 1/4" reel-to-reel and divided the tape path into 8 individual record tracks. This allows for 8 individual sources to be recorded separately and mixed down to a stereo image later. Each track took up 1/8 of the tape width, or 1/32". A 1", 16-track recorder meant that each track took up a 1/16" path on the tape.
Modern digital recorders obviously don't use tape, and "tracks" are actually recorded as separate data files, but the analog terminology works so well that there's no need to change it.
So your 6-input, 8-track recorder can take 6 separate sources and record them separately. Since it's 6-in, 8-track, my assumption is that the last two tracks record a stereo mix of the first 6 tracks. This describes the Tacam DR-680.