  We investigate Einstein-Gauss-Bonnet (EGB) 4D massive gravity coupled to
nonlinear electrodynamics (NED) in an Anti-de-Sitter (AdS) background and find
an exact magnetically charged black hole solution. The metric function was
analyzed for different values of massive gravity parameters. We verified the
first law of black hole thermodynamics and the generalized Smarr formula,
treating the cosmological constant as thermodynamic pressure. Vacuum
polarization is defined as the conjugate to the NED parameter. To analyze the
local stability of the black hole, we compute specific heat. We investigated
the Van der Waals-like/reentrant phase transition of the black holes and
estimated the critical points. We observed small/large black hole (SBH/LBH) and
small/intermediate/large black hole (SBH/IBH/LBH) phase transitions. The
Joule-Thomson coefficient, inversion, and isenthalpic curves are discussed.
Finally, the minimum inversion temperature and the corresponding event horizon
radius are obtained using numerical techniques.
