Copy to the other side will give you exactly the reverse of your design, if that's what you want.
However, if you have a design on the left side, and want to put the same thing on the right side, select all the layers of the design and then Save As . . . New Vinyl Group, giving it a recognizable name. Then move to the right side, select an unoccupied space in the design boxes on the lower portion of the screen and load up the Vinyl Group.
That's my terms off the top of my head. There is a more detailed description in the first post of this thread.
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