For the moment, let's not even start the discussion about the "plumbe quick" rubber sleeves, vs. the banded couplings. There are issues here, but I digress.
First, what is that stack you are cutting into? If it is carrying waste from an upper level, then you need a vent for the washing machine. And where is the trap for the washing machine standpipe?
Now, if your drains are ABS, you will save yourself some hassle by just using ABS for the washer hook up. But we need to answer those questions above.