If we look at carbons 1 and 2, they have 5 electrons. 3 are directly involved in bonding, and 2 are involved in delocalisation to create the 2 benzene rings. This would mean that they had 5 valence electrons, which isn't possible, and thus there should be only one benzene ring.
Chemists are already accustomed to this type of formula, even though it is not absolutely correct. More exact would be drawing all bonds with double solid/dashed bonds to express that the bond order is between 1 and 2, approximately 1.5, but is almost never done
Rarely can be seen formula with the two circles merged (and maybe dashed also), like
But the electrons are in fact delocalized across all bonds of the polycycle structure in "electron cloud" that looks somewhat like the infinity sign ∞ in this case (naphthalene) above and below the planar molecule. What matters is that the count of π (those from the "second bond" of the double bond) electrons is 4n+2 for n is some natural number (here it is n=2). It is a special feature called aromaticity, which has something to do with advanced topic of quantum chemistry; and it greatly stabilizes the molecule. Any of these formulas is unable to describe reality.