A fid helps make it a lot easier, I used a pair of forceps for years, but now use a fid. Start with purchasing a
5/8” fid. The fid is 5/8” for the OD, it is for use with 3/8”/10mm rope. The easiest way to describe it to unbraid the end with the hook, you want to remove the metal for the extension. If you feel the rope near the current loop you can feel the end of the rope is pushed inside the hollow part of the rope. Go 12-18” beyond that and start pushing the rope together working your way to the hook, it will accordion together freeing the end inside, watch how it comes apart and you can see how it is weaves through itself and then fed inside the hollow part of the main rope. Attach the end of the rope to the fid and work it back through in reverse of how it came apart and form a loop. This was how I taught myself to do it long before there was YouTube.
At that point cut the lug off the other end and the red cover will slide off. Mimic the work done on the other end and make a loop. I would make the loop a little larger than the first end. There’s also a bunch YouTube university out there, just search splicing winch rope. Once you learn this skill there is a bunch of things you can do with it, I make all kinds of short ropes, even custom ski ropes and moring lines for boats.
Side note, I use the red cover as a chafe guard for the loops.