I am planning to relocate an old receptacle to a new wall location in our house. If I will splice a new wire to the old one and put it in a box, should that box be visible on the wall(with cover plate) or can I just hide the box inside the wall. Thanks.

Not sure about your local regulations but usually you cannot hide a box in the wall, it always has to be accessible. Always best to avoid splice and use one run if possible.

I agree that one continuous run is the best, but that is not always possible. Local codes probably don't apply here-I believe the NEC requires that any time a run is spliced in a box, or runs through a box then to another circuit, the box must be accessible. This provides access to the splice if there is one, and also provides
The ability to pull new wires for the addition of a new circuit(s). I had to do a lot of rewiring on my house and did the cover plate in several locations. I don't see this too often in houses but see it a lot in commercial buildings. I'm sure TK Russell will be able to give you the facts per NEC, he know's his stuff.

If for some unknown reason you did make the splice in the box and then cover over the plate I would solder the joints before I taped them, and I would double tape them after putting wire nuts on. Then I would make some reference somewhere, in the house plans or in a journal, as to where the junction is and what it supplies.

Burying splices, even if done correctly in a junction box with a cover, is never allowed by NEC. I can guarantee that there will be a problem in the future, per Murphy's Law, with these splices.

I have spent many hours on service calls, all very billable, searching for splices buried in a box someplace, which had failed and caused outlets and lights to stop working. This is the best condition, hopefully the splices do not heat up in the wall to create a fire hazard.

Perhaps the cable that is too short can be dropped down into the basement, or brought up into the attic, there a splices can be made in a box, and this would be considered accessible. Other wise make the splices in a box that is supported with box supports in the drywall, and cover the opening with a finish flush plate, that can be painted or wallpapered to try to make inconspicuous as best as possible.

TK,
Thanks for posting. I was 99.99% sure that the box had to be accessible. In my reply it maybe sounded like I used a cover plate then buried the box. Nope. The boxes are either in the attic/basement, but I did have to do some in the wall in the manner you suggested.