The total number of aromatic compounds/species from the following is

A species is aromatic if it is cyclic, planar, fully conjugated (continuous cyclic overlap of $p$-orbitals) and contains $(4n + 2)\,\pi$ electrons (Huckel's rule). Let us analyse each species.

$1,4$-Benzoquinone:
The six-membered ring has only $4\pi$ electrons (from the two $C=C$ bonds); the two $C=O$ groups are cross-conjugated and do not contribute to a continuous $(4n + 2)\,\pi$ ring system. Hence, it is non-aromatic.

Tropylium cation:
A planar, cyclic, fully conjugated seven-membered system with three $C=C$ bonds and a positive charge (empty $p$-orbital). It has $6\,\pi$ electrons, satisfying Huckel's rule with $n = 1$. It is aromatic.

Phenanthrene:
A fused tricyclic, planar, fully conjugated hydrocarbon with $14\,\pi$ electrons. It obeys Huckel's rule with $n = 3$. It is aromatic.

$1,2$-Dihydronaphthalene:
It contains an intact benzene ring fused to a partially saturated six-membered ring. Because of the benzene ring, the molecule as a whole is classified as aromatic.

Cyclobutadiene dication:
A planar, four-membered ring with one $C=C$ bond and two positive charges (two empty $p$-orbitals), giving $2\,\pi$ electrons. It satisfies Huckel's rule with $n = 0$. It is aromatic.

Cyclohexadienyl anion (as drawn with a $-CH_2-$ group):
The $sp^3$ $-CH_2-$ carbon breaks the continuous cyclic conjugation, so the ring is not fully conjugated. Hence, it is non-aromatic.

Counting the aromatic species: tropylium cation, phenanthrene, $1,2$-dihydronaphthalene and cyclobutadiene dication give a total of $4$ aromatic species.

Hence, the correct option is $(2)\ 4$.