I have a flower garden that was overwhelmed by what we called snow on the mountain after sacral failed attempts to get rid of it I resorted to putting black plastic down and trying to kill everything that was last summer today I pulled the plastic off and found plants growing under it. Not sure what I. Should do next

There is a plant called Snow on the Mountain, a type of Euphorbia. Can you post photos of your plant?

I haven't been able to make plastic work either.
I've had a run-in with an aggressive euphorbia...

But I suspect OP is dealing with Goutweed:
https://www.maine.gov/dacf/mna...

My condolences, but I can't really think of much you can do unless you would like to try spreading out some wall to wall short fiber carpet on top of the plastic, and then spread mulch on top of that, and line up your pot jungle on top of that...

Not sure that putting a driveway on top of the problematic stuff would even work.

Blocking light and covering with an old rug works much better. Smothering with lack of light AND lack of good air exchange is like a double whammy.

If this is goutweed as has been suggested it is difficult to remove. It has deep rhizomes which need to be dug more deeply than regular weeds. Because of the depth the rhizomes are not as quickly affected by covering with plastic.

I hate to suggest it but this seems like the time for glyphosate. It will kill the rhizomes and will breakdown so you can replant.