  The neutrino trident scattering process in neutrino - tungsten interactions
at the LHC energy regime is investigated, and the cross-sections for different
leptonic final states in coherent and incoherent interactions are estimated.
Furthermore, the associated number of eventsat FASER$\nu$2 detector is
estimated considering different predictions for the flux of incident neutrinos
on the detector, based on distinct hadronic models for the particle production
in $pp$ collisions at ultra-forward rapidities. Our results indicate that the
observation of the neutrino trident process is, in principle, feasible at the
Forward Physics Facility.
