= Solution
For a monocyclic, approximately planar, continuously conjugated pi system, <Hückel's rule> predicts aromatic closed-shell filling for $4n+2$ pi <electrons>, with $n=0,1,2,\ldots$. Every atom on the circuit must have an appropriately oriented orbital; counting <double bonds> without checking <pi conjugation> is insufficient.
\b[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. \b[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.<Structure of xanthone by Shigeki Onuma and others>[1990, pp. 1725–1727, molecular geometry]{ref}
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