I d suggest making the loo.
Tie washer drain into sink.
Position the end of the drain midway between the washing machine and sink if they are less than 10 feet apart.
The washing machine drain 1 5 would run horizontally along wall pick up the lavatory drain still 1 5 and wye into a 2 drain with the shower which then wyes into a 3 drain with the toilet and on to a sump.
Smaller drain lines will not accommodate the.
You may need a special drain hose depending on the distance of the washer to the sink.
Third the pipe from the sink to the.
You can install a bracket or wire ties on the back of the sink so the washer drain hose is permanently attached to the sink.
It is not allowed to share a sink drain.
I used a coat hanger to secure the washer drain hose from flying out of the utility sink and spraying all over the basement floor.
Do not tie it into the trap.
Glue a 2 inch abs double sanitary tee to the drain inlet using abs cement.
Something like this or this but in reverse.
Laundry sink waste ties in below the standpipe tie in.
Answer if you can install your washing machine in the garage and next to a utility sink then yes you can let it drain into the sink.
Second the place where the connection is made between the sink drain and the washer drain must be lower than the bottom of the s shaped pipe under the sink.
The reason we made the comments we did is that under most codes the washer drain must be 2 and tie into a larger drain.
The sink drain may be wet venting the toilet which will then create problems for the toilet and the sink.
Tee wye off the vent for the sink above the standpipe waste at least 42 off the floor and if sink on the left in this photo then above the laundry box.