A washing machine drain can begin in a wall, but must eventually end up beneath the floor or it should terminate into a "sewer-lift" or pumping system. Code requires that the washer drain be a minimum of two-inches in diameter. A p-trap must exist in the line and is normally located within the wall behind the washer and about twelve-inches above the floor. From that point the drainpipe can travel in any direction you wish as long as it drops (per code) at least one-eighth-inch per foot. We prefer a quarter-inch or more. The greater the fall (in the drainage slope), the less the chance for clogs. If you intend on running the line through a wall you must be sure that you do not destroy its structural integrity by drilling massive holes through all of the studs. If it were our house we would run all of the waste lines that begin in walls immediately down and through the floor. And, good luck!