Given any set of two distinct letters (neither of which is O) and two distinct digits (neither of which is 0), we can build exactly one license plate because, whatever the letters and digits, there is only one allowed order. We can choose two distinct letters (excluding O) in $ \binom{25}{2} $ ways and two distinct digits (excluding 0) in $ \binom{9}{2} $ ways. Thus the total number of license plates is $ \binom{25}{2}\binom{9}{2} = \boxed{10800} $.