I can't see why you would want to do this - most people struggle in the other direction trying to make their objects 'solid'... BUT assuming it has some hidden use we can't think of... a small hole will make it 'non-solid'... if you want all 6 faces of 'the box' to remain the same, but for it to be 'non-solid', you must add something else into its group/component like another group - e.g. group one of its faces - or add a single diagonal non-faced internal line that is then hidden - use Xray mode [or put it on an off-layer]. A manifold 'solid' contains no entities other than faces and their edges, and every edge must have two faces - no more, no fewer - it's a simple rule [note that for these purposes 'guides' are ignored]. So the converse is true - to make something 'non-solid' you must ensure that the simple rule is broken!

Does your green squares a copy past of a same component? Can you post your file in V6? (save as)

I wouldn't even consider Copy and Paste for this. I would only use Ctrl/Move (or Option/Move on Mac) for this kind of thing.