Drill the appropriate size holes in the metal faceplate for your female audio connectors, using your metal hole saw bit. Leave enough space between the holes to keep the audio connectors completely separated. Also, drill a hole anywhere on the metal faceplate that is the appropriate size for your small bolt to fit through. You may also need to drill holes for the screws that attach the metal faceplate to the junction box.
Fasten your female audio connectors to the metal faceplate, using the holes you drilled.
Drill a hole big enough to fit your multi-core snake cable through the side of the the junction box, if necessary. Some metal junction boxes come built with a hole for this purpose.
Slip enough of the snake cable through the hole in the junction box to allow you to work freely with the wires.
Use the utility knife to cut away some of the outer insulation from the junction box end of the multi-core cable, exposing the bundle of colored wires inside of it.
Strip the insulation from the ends of the colored wires that you will be using for your audio connections.
Attach and solder the colored wires one by one to the audio connectors on the back of the metal faceplate, taking care to make sure none of the bare wires are touching each other.
Solder a short ground wire to only one of the audio connector's ground terminals, preferably the one nearest to the hole you drilled in the faceplate for the small bolt.
Strip the free end of the ground wire and crimp the loop or fork grounding wire connector to it.
Slip the small bolt through the front side of the hole you drilled for it, and then fasten the loop or fork grounding wire connector to the backside of the metal faceplate with the nut.
Cut away about 6 feet of insulation from the free end of the multi-core snake cable.
Sort the colored wires in the bundle by the audio connectors they are attached to at the junction. Wrap each individual set of wires with electrical tape, leaving enough wire to attach the male connectors.
Strip the insulation from the ends of the colored wires.
Attach and solder the colored wires one by one to the male audio connectors, being careful to use the correct colors for the connections.
Solder a ground wire to the male connector that corresponds with the female connector to which you connected the ground wire in the junction box.
Strip a little insulation from the free end of the ground wire you just attached, and crimp a loop or fork connector onto it. The ground wire is to eliminate any ground loop between your mixer and the junction box. When you install the audio snake into your setup, you will attach the ground wire to the grounding screw on your mixer.
Test the wires between all the male connectors and the corresponding connections at the junction box. You may even want to plug in some audio connections and test them to be sure you've wired the connectors correctly.
Wrap the remaining exposed colored wire at the male connectors with electrical tape.
Pull most of the multi-core cable's slack out of the junction box, then attach a cable stopper clamp to the snake cable just inside of the junction box so that the slack can't be accidentally pulled out of the box. Attach the other cable clamp to the multi-core cable just outside of the junction box to prevent too much slack from entering it. Make sure you don't pull any of the soldered connections loose from the back of the faceplate.
Tuck the colored wires carefully into the junction box, and fasten the metal faceplate to it with the screws.
Test the audio connections one more time.