I am terribly embarrassed because I don't quite understand what you mean on how that connection is supposed to work. Is there perhaps a picture or diagram you can find that might illustrate what you want me to do? Or maybe you can find the type of cable you're talking about to show me a picture of that? Thank you so much for helping me!
Your photo of the back of the Akai amp shows two short metal links that connect the left and right pre-amp outputs (PRE OUT) to the left and right main amplifier inputs (MAIN IN). Remove them. The receptacles in this photo are called RCA jacks (female), and they accept RCA plugs (male).
To add the subwoofer while also connecting the PRE OUT to MAIN IN, install 2 RCA splitters, for the left and right channels. They can look like either of these (below). Insert the RCA plug side of the splitter into the PRE OUT jack on the Akai back panel.
Conect one of the splitter's RCA jacks to the MAIN IN jack on the Akai back panel, using a short RCA cable. (Standard RCA cables have male RCA plugs on each end.) And connect the splitter's other RCA jack to the appropriate RCA jack on the subwoofer, with a longer RCA cable. Do this for both left and right channels.
You can find inexpensive splitters and RCA cables (also called patch cords) at
Amazon or
Monoprice, or other sources. Between the RCA jack/plug variations, and the different cable lengths, it can be confusing.
Splitter Y adapter (first photo)
Short Y cable adapter (second photo)
Here are two examples of RCA cables, one is
1 foot long, and the other is
6 feet long. You should be able find cables long enough to reach your subwoofer.