Best way to affix plywood to wood unit?
Take a look at a French cleat, it will help keep the ply level and supported and will allow you to 
remove whenever you wanted provided you can lift the plywood off the back.  

The two factors here, one are getting the cleat affixed to the ply and the entertainment back, ideally both 
have enough depth for wood screws. The second is the gap between the ply and the entertainment center the cleat will create.