(B) To determine aromaticity,a species must follow $H$ückel's rule ($4n+2$ $\pi$ electrons),be planar,and have a fully conjugated system.
$(A)$ Cyclohexa$-2,4-$dienyl cation: This species has $4$ $\pi$ electrons. It is not fully conjugated because of the $sp^3$ carbon atom. It is non-aromatic.
$(B)$ Naphthalene: This is a polycyclic aromatic hydrocarbon with $10$ $\pi$ electrons ($n=2$ in $4n+2$). It is planar and fully conjugated. It is aromatic.
$(C)$ Tropone: The oxygen atom is more electronegative than carbon,pulling electron density towards itself,which creates a resonance structure with a tropylium cation ($7$ carbons,$6$ $\pi$ electrons). This makes it aromatic.
$(D)$ Cyclohexa$-1,3-$diene: This has $4$ $\pi$ electrons and is not fully conjugated due to $sp^3$ carbons. It is non-aromatic.
Therefore,only $B$ and $C$ are aromatic species.