Is a quinone ring aromatic? I'm trying to work out which are the aromatic ring systems in the drug aklavinone: 



I am trying to follow Hückel's rules that the compound must be cyclic, be planar, possess a p-orbital on every atom in the ring, and have a π-system with $4n+2$ electrons.

I see that the benzene rings are obviously aromatic. But does the quinone ring (in red) also count as part of the 'aromatic ring system'?
Strictly speaking, once we have anything more than a single cycle without conjugated side chains, the Hückel's rule does not really apply, and the very definition of aromaticity becomes somewhat muddy. But that's not an answer they expect from you, anyway. So just point to the first and third rings and call them aromatic, and that would be it.

Why not the second? Well, because the quinone fragment is not aromatic. Its bond length are different from each other. These $\ce{C=O}$ bonds are always double, and the $\ce{C-C}$ bonds next to them are always single; you can't draw a resonance structure where that would be otherwise.