Phenanthrene is a polycyclic aromatic hydrocarbon consisting of three fused benzene rings. It has a completely conjugated system with 14 $\pi$ electrons (from 7 double bonds). According to Hückel's rule, a ring system is aromatic if it has complete delocalisation of $(4n + 2)$ $\pi$ electrons, where $n$ is an integer ($n = 0, 1, 2, \dots$) .

By equating the number of $\pi$ electrons to Hückel's formula: $4n + 2 = 14$ $4n = 12$ $n = 3$

Thus, the value of $n$ is 3.