Sorry for the late response, but from your question it kinda sounds like you are thinking to pipe your washing machine discharge line directly into the sewer line. And I cannot tell for sure by your picture, but it appears to be in the basement with a cast iron toilet branch draining into the cast iron stack before it changes to PVC which would make that fitting with the red dot on it just below the floor above. Is all that right?
Please note that a washing machine cannot be "hard piped" into a sewer line. You need a washer standpipe with a P-trap before connecting to the PVC stack. That P-trap will also need to be vented to the main vent above the last branch line going onto it or vented separately. And if it is vented separately, you can run a 1 1/2" vent pipe through your roof or out the side of your house to above your roof, although you may be able to stop it before the top of your roof depending on various conditions that have to be met. Or you can use an Air Admittance Valve (AAV), again meeting certain conditions for that installation.
Your connection to the stack should be a 2" reducing sanitee, although a 2" reducing wye connection is preferred by many with these high-volume flow washing machines, and the washer standpipe and P-trap should be all 2".
And before you cut the PVC stack to install anything, be sure the cast iron stack above the PVC is supported. As someone has installed PVC below the cast iron, I would assume someplace in attic you will find a pipe clamp that is resting on the ceiling joists to keep the heavy cast iron from dropping when that PVC was installed.
Here's a couple of washer standpipe pics. One has an AAV, and the other shows a 1 1/2" vent that either ties into the main vent in the attic, or goes up through the roof as its own vent, or routed out the wall and up to the roof outside the house
