Do or you mean the A3440S? I ask because I have one. The best view I can immediately find of the mixer shows it is equipped with RCA phono unbalanced input and output connectors for line* in and output signals. Mic inputs are on 1/4" jacks. (ask again if you want to get XLR mics into the mixer or indeed the tape deck)
So, assuming both pieces of gear are working properly AND you have a handful of RCA to RCA cables I cannot for the life of me understand why you cannot exchange audio between the two devices! Line outs back of tape deck go to line ins on the mixer. Line outs of the mixer go to line INs on the deck. I assume you listen on headphones plugged into the mixer?
I shall have a search but if you can find a link to a manual for the mixer that would help. I know the A3440s like the back of my hand.
*These will be at the "prosumer" operating level of -10dBV, or 0.316 volts rms (if you don't know what "rms" means, boy you have a lot to learn! "Professional" op level is usually +4dBu, about 1V rms. Pro systems have a wider dynamic range because +4dBu is well above noise but since this is tape that is by far (like 30dB!) the limiting factor.
Dave.