What you have there will work.
The 90 under the sink santee needs to be a long turn 90.
You can also run it out horizontal and use a combo on it's back for the sink vent.
The washer is 2" waste, 2" trap and standpipe, and 1.5" vent
The sink is 2" waste, 1.5 trap, and 1.5" vent
Pictures here need to be 800 pixels or less.