As we can see from the image, that is the positive battery cable which has had it's lining melted. Clearly this should not happen. Previously the cable was compressed against the compressor line where you can see blackened metal. Obviously, the AC is not functioning right now. Kind of need AC now that we are getting into the middle of Summer. Any ideas what happened here? And how it would be fixed?

 

Not sure what you're asking? Obviously fix the wire, fix the A/C tube if damaged, and make them not touch each other.

 

A/C lines are not gonna get anywhere near hot enough to melt that. That likely melted from either a poor connection or something drawing A LOT of power, something like car wouldn't start and it was cranked excessively.

Change the wire and clean all the connections and then get ready for the wild ride of fixing a non working A/C system.

 

The wire has probably been rubbing there for quite a while, once it wore thru, the wire shorted to the a/c line. That WILL generate enough heat to burn stuff..... (and I am surprised the truck would continue to run......)

But, as said, replace and re-route the wire.