What cable is this and what guage should I buy?

[Fairtax4me]

Ok, sounds like you're on a good start then.

[LEMANSZ20]

so to confirm, 10 guage if anything to replace that wire? For now im not gonna replace it, im gonna try the white ones.

[Fairtax4me]

Yes 10 gauge if you decide to replace it. I’d shorten up the white one that’s there already and use that.
Shorten that white wire to about 8” long and move it to the FnR switch. The bottom terminal of the FnR switch (w big red cable) is exactly the same as the pack positive, so there’s really no need to run the wire all the way from the receptacle to the battery. It also makes one less connection at the battery post to cause problems.

It appears the previous owner has also moved the reverse power wire to the pack positive.
On the FnR switch Forward power goes to the lower left terminal, reverse power goes to the lower right terminal.
Pulling reverse power from the pack positive will give the cart full speed reverse.
Normally with that cart, power for reverse would come from the positive of battery 4, which would provide only 18v for reverse power, which makes it slower, about half speed.
You can pull power for reverse from battery 4 (18v), or battery 3 (24v) if you prefer a slower speed/less power for reverse.
If you want to keep full speed reverse, you can ditch the cable going from the bottom right terminal of the FnR switch to pack positive, and simply use a jumper bar or short cable across the two bottom terminals.

[LEMANSZ20]

I appreciate the help, I have the diagram but it gets confusing I dont play with wiring to often.