Need advice for laundry drain

[Charlie U]

Hi there. DYI homeowner here looking for advice how to properly vent and drain - and solve a tricky situation.

I'm converting a small bedroom into a laundry room. As you can see from the photo below, there's a bathroom on the opposite side of the wall, and it's 14" lower than this room. The white PVC pipe is the drain and vent for the bathroom sink. I would think I can replace the singe tee with a double and add a p-trap for the laundry box, but it would be LESS than 6" from the floor, which I believe is minimum requirement. So I'm at a loss as to how to drain and vent both the laundry and sink properly. Any advice is greatly appreciated!

 

[Terry]

You can add a second vent for the washer drain and raise the p-trap that way.
Two lines coming up, one for the lav, one for the washer. Each one vented and tied together again at the horizontal going back to the cast.