 Solution

For a monocyclic, approximately planar, continuously conjugated pi system, Hückel's rule predicts aromatic closed-shell filling for $4n+2$ pi electrons, with $n=0,1,2,\dots$. Every atom on the circuit must have an appropriately oriented orbital; counting double bonds without checking pi conjugation is insufficient.

The two outer benzene rings are clearly aromatic; the central pyrone ring has a weaker, polarized six-pi aromatic contribution. Each outer ring has the familiar six-electron circuit. For the central ring, a useful charge-separated contributor moves the exocyclic carbonyl pi pair onto oxygen and donates one endocyclic oxygen lone pair into the ring. Its four fused carbon p centres contribute four electrons and the ring-oxygen lone pair supplies two: a six-pi, pyrylium-like circuit, with positive charge on the ring oxygen and negative charge on the carbonyl oxygen. This does not make three independent benzene rings of equal aromatic stabilization; localized carbonyl bonding and the fused benzene circuits remain important contributors.

The three oxygens play different roles. The endocyclic ether oxygen donates a p-type lone pair to pi conjugation. The carbonyl oxygen accepts pi density in the charge-separated contributor. The phenolic oxygen donates into the outer ring as a substituent. Its in-plane lone pair is not an extra pair to add to every ring's electron count. In particular, neither the external C=O pair nor both lone pairs on a ring oxygen should be counted as independent extra ring electrons. Structural studies of xanthone support a largely planar conjugated framework, while the division into strongly aromatic outer rings and a more polarized central ring is an electronic-structure interpretation.^[ref]