Grab your 2 sheets of acrylic. I got mine at the hardware store and the size worked perfectly so no cutting required.
Keeping your two sheets aligned, tape the edges with painters tape. This will also prevent scratches when you drill... slowly drill a hole through both sheets of acrylic.
These simple pieces of hardware are all you need (x4): cap nuts, nuts, and lag bolts.
The extra nut makes sure that the cap nut and the lag bolt tightly pinch the two pieces of acrylic together.
To hang, wrap some picture wire around the back two lag bolts on the back of your floating frame... if you don't care for the visual wire, you can make 2 smaller loops (separate) and wrap these individually around the back lag nuts.