Backstory: I had a pair of headphones with a faulty 3.5mm plug on one end, and a 3.5mm audio cable that was so long, it picked up an insane amount of interference.
Solution: Cut both cables! Join them together! Reduce, reuse!
Problem: What do I do next? (See photo.) I’m not sure which inner wires connect to which, and I’ve never seen wires like in the headphones before; they don’t seem to be really individually insulated, but appear to be dyed copper woven with some sort of fiber.

(The left cable is from the Sennheiser headphones; the right, from a cheap 3.5mm audio cable.)