  Discrepancy between the measured value and the Standard Model prediction of
the muon anomalous magnetic moment is a possible hint for new physics. A
$Z^\prime$ particle with $\mu\tau$ flavor violating couplings can give a large
contribution to the muon anomalous magnetic moment due to the $\tau$ mass
enhancement at the one-loop level, and is known to explain the above
discrepancy. In this paper, we study the potential of the Large Hadron Collider
(LHC) for detecting such a $Z^\prime$ boson via the $p p
\to\mu^-\mu^-\tau^+\tau^+ $ process. Earlier studies in the literature only
considered the production channel with quark initial states ($p p \to q \bar q
\to\mu^-\mu^-\tau^+\tau^+ $). Here, we show that the photon initiated process,
$p p \to \gamma \gamma \to \mu^-\mu^-\tau^+\tau^+ $, is in fact the dominant
production mode, for a heavy $Z^\prime$ boson of mass greater than a few
hundred GeV. The potential of the high luminosity (HL) LHC is also considered.
