Measure the width and depth of the stacked laundry machine's base.
Cut a rectangular piece of 3/4-inch plywood, equal to the measurements from Step 1, plus 2 inches added on all sides. For example, if your initial measurement was 36 by 28 inches, the sheet's dimensions would be 38 by 30 inches.
Cut four 2-by-4-inch boards. Two boards should be equal to the width of the plywood sheet, with the other two boards 4 inches less than the depth. For example, if the plywood sheet measures 38 by 30 inches, two boards will measure 38 inches and two will measure 26 inches.
Arrange the 2-by-4-inch boards in a rectangle -- resting on the narrow sides of the boards -- that's equal to the dimensions of the plywood board. Screw the boards together with 4-inch wood screws, using two screws at each point where the boards intersect.
Place the plywood board on top of the rectangular frame. Screw the board to the 2-by-4-inch frame with 2-inch wood screws spaced 4 inches apart.
Place a caster wheel at each corner of the plywood base and secure them with screws. Turn the platform over. Lift the stacked laundry machine onto the movable platform. The 2-by-4-inch boards will ensure the machine doesn't slide off the platform.