Those things are a pain in the ass.
Spin off the entire valve so you can hold it in your hand.
Press the new plastic piece into the valve hard as fuck with the other hand, then start to screw the 4 screws on the side.
Just gotta press it into the valve real hard & tighten the screws. Thats it.
And make sure the rubber gasket thingy is snug.
Just realized the way I wrote this makes it sound like you need 3 hands
I did it the other day & pinned the valve in a corner by the sink & pressed the plastic piece into it. Then tightened the screws.