Type-X two-Higgs-doublet model in light of the muon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo>?</mml:mo><mml:mn>2</mml:mn></mml:math> : Confronting Higgs boson and collider data

The recent Fermilab measurement of the muon anomalous magnetic moment yields $4.2 \sigma$ deviations from SM prediction when combined with BNL E821 experiment results. In Type-X two Higgs doublet model, we study consequence imposing observed $g-2$, along constraints theoretical stabilities, electroweak oblique parameters, precision data, and direct searches. For a comprehensive study, scan whole parameter space in scenarios, normal scenario where $h_{\rm SM} = h$ inverted SM}=H$, $h$ ($H$) is light (heavy) CP-even boson. We found that large $\tan\beta$ (above 100) pseudoscalar mass $M_A$ are required to explain $g-2$ anomaly. This breaks stability unless scalar masses satisfy $M_A^2 \simeq M_{H^\pm}^2 m_{12}^2 \tan\beta \approx M_{H/h}^2$. search bounds at LEP LHC exclude $A$ window $M_A \lesssim 62.5~$GeV. also show electron consistent model prediction, but lepton flavor universality data $\tau$ $Z$ decays not. separate exploration propose golden mode $pp \to A h/AH 4 \tau$ HL-LHC.