When the washing machine is on and when the water is discharge out the floor drain ovewrflows. The house is only 2 years old. (septic tank system)

You didn't just purchase a New washer did you? Like a Maytag?
If you have no other backups, (like when you flush) then you have a partial blockage downstream from the floor drain. Let's check the septic tank. Locate and open the house cleanout. Now cycle the washer. Does the pipe fill up? Yes? You either have a tank that's so full that it won't handle the extra volume your washer pump puts out or a blockage in the sewer line. No? Then the blockage's will be found in the house main and should be snaked from the washer stand pipe or the washer roof vent. Good luck, Tom