We just moved into a new house, and the wall mounted washing machine "box", that contains the hot/cold water connection and a standpipe for the drain, currently has a plastic cap covering the drain pipe. The cap has a cylindrical protrusion, which looks like it might be used for turning the cap with a special tool, maybe? In any event, initial attempts at removing the cap were unsuccessful, and I don't want to risk cracking the pipe, so I'm asking what the typical procedure is in this case?

Thanks for any suggestions!

There is nothing visible that indicates the make/model of this wall unit.

First it just might not have a drain line attaced so the first thing I would check is to make sure a drain line runs to that wall box. If you have a basement this is usually a easy job. Some of the wall boxes have knock outs and some have pop out plugs. Post a good picture so we can see exactly what you have.