Hello, thanks for the suggestions. Unfortunately, I was not very clear. I would like to transform my garage into a kitchen. My current kitchen sink is on an exterior wall. I would like to make my current kitchen a laundry room. The washer, in the garage is on an interior wall which is directly opposite a bathroom. It is not vented through the roof, there is a pipe sticking out of the slab. So, I would like to put my washer along the exterior wall where my k.sink is now and my k.sink along an interior wall where my washer is now. The current kitchen and garage are perpendicular to each other and do not share any common walls.

Thanks
Nathalie

I hope you're experienced in plumbing and have the necessary tools to do the job.
The current exterior kitchen will have to be opened up and a washer trap and stand pipe installed. If the kitchen stub out tee is set back far enough in the wall you may cut the stubout back and cap it off without removing it. You may run the existing hot and cold lines up to 1/2" drop eared ells and, after securing them to the wall, install 1/2" boiler drain valves on them for your washer hook up.
Before you can even start on the sink you MUST know the function of that pipe sticking out of the slab. You will also have to run a vent for that sink but until you can find out what that pipe does, don't touch a thing.
What you wish to do is considered a major plumbing remodel job so I suggest that before you start that you call in plumber and be guided by his advice.

As long as you are using the existing supply and drain pipes where they are, but only for different uses, I don't think it should that big of a deal. Likely all 3 pipes in each location are in a single wall cavity. Shut off the water and remove the sink and washer. Use a utility knife, not a box cutter and slice the drywall down the middle of the stud on each side of the cavity. Often you can spot screw heads over the stud. There are also stud finders. You can also keep pounding a nail in until it hits a stud. The other one should be 16 inches away. Once you have removed the drywall in both locations as high as the washer fittings, study the pipes. If everything was working OK before, chances are you already have the vents and traps you need. You may be able to cut off the existing pipes at one location and splice them back on at the other. How easy that will be, will depend what they are made of and your skill and tool collection. You might unsolder a joint and move the whole pipe.

Maybe the best thing is to get caught up on laundry, and remove the washer, and then the dry wall to expose the pipes. Identify them, and if you need to, come back for instruction with working with them and also study what is available. Usually you can look around the plumbing section at Lowe's and figure things out without anybody bothering you. If you need laundry before the job is finished, you can always hit a laundromat. Once you take pipes apart beyond any shut offs, you must finish all back to a shut off before you can use any water. Anywhere. Adding shut offs where you lack them is a good idea. I always use ball valves if I can. I like their 1/4 turn convenience and freedom from leaks. I just saw some hose bibs today with them.

Once things are piped up, replace any insulation you disturbed and add new drywall. Tape, mud, and paint.