How do I duplicate a layer and move an entire moving item and its frames around?

I’m trying to imitate what Mr Mislav did in his Simple Grass Animation and somehow I can only move a single item and not its moving versons

Trying to do what you said, somehow still can’t do it, or I’m doing something wrong

I can duplicate layers, but How do i properly move it all to the side, so I can have two grasses?

I was able to do it?

Simple Grass Animation

I think I did it

Simple Grass Animation