Can a landlord collect double rent in the state of Virginia. Example: We broke our lease, gave a 60 day notice and agreed to forfeit our security deposit. Our rent was paid until the end of the month, however we moved out on the 17th, so the new tentent's could move in on the 24th. We did not turn off the utlities until the 24th.

The landlord does not think that they have to return the rent we paid from the 24th through the 31st of August. I believe it is the law in Virginia (and most states) that the landlord can not collect double rent.

Who is right?

Since your rent was paid up the security deposit should be used for any itemized damages the landlord might deduct (place left filthy, needed painted, needed new rugs, etc... )
I am assuming you are saying you broke your lease for the month your lease was up. Otherwise, it depends how it was written in your lease.

I'm sure your landlord is saying you are not getting any money back for other fees - such as ad costs, make ready maintenance issues - you should not be concerned for 6 days rent as your landlord seems to have issues with how you left the property.