Is there an easy fix for this? From what I can see, looks like I have to remove the handlebar tape, and route the cable from the handle bar through the casing etc like new. I got the bike from the "direct" "bikes" store. Did not expect this. One of the brakes is working and the other has this issue and no action.
Personally, I'd recommend a new inner cable from the shop.
That is your brake that you are playing with and how important is it that they work when you use them?
There will be a you tube video on line on how to replace an inner cable, and it's not too difficult, as it's a normal service procedure
You probably won't need to unwrap the bar tape - simply release the inner wire from the pinch nut/bolt on the brake, possibly pull off any end cap crimp, and pull the wire all the way up and out.
Retwist any loose strands of brake cable so it lies flat. I suggest you use a drop of superglue now on the very end to keep it all together. When set, carry on.
Then squeeze that brake lever, peer down the hole and feed the glued end through the brake's stop, and then into the inner cable. It may go easy, it may take a very long time to get it in the hole you can't see... there is no guarantee that the holes line up.
One trick is to use another length of brake cable, and feed it up from below temporarily. Then when you see it come up into the brake lever, use that end to guide the proper brake cable into the unseen outer.
If you can't get it within 10 minutes, give up and unwrap the bartape on that side. It should unwrap from the middle so its not too bad. You'll probably need some tape to close it up again when done. It may help to very-slightly dirty the bar tape before unwrapping, so you can see where they overlapped. Perhaps a pencil dragged across the underside of the bars where it can't be seen.
When you do get the wire through, remember to seat it in the brake's pinch bolt, and adjust the brake as required. And test before riding.