  The recent observation of the muon $(g-2)_{\mu}$ anomaly continues to
challenge the explanations provided by the Standard Model. However, this
anomaly can potentially find reconciliation within the framework of two-Higgs
doublet models, provided that the pseudoscalar mass remains low. The
introduction of additional fermionic components, such as a generation of
vector-like quarks, not only broadens the acceptable parameter range for
elucidating the anomaly but also presents an opportunity to circumvent
conflicts with constraints from B-decays and heavy Higgs searches. We
demonstrate the efficacy of fitting the anomaly in the muon magnetic moment
within these models, assuming that vector-like quarks do not undergo mixing
with Standard Model quarks. With interactions following a type-X pattern for
standard model quarks and a type-II pattern for vector-like quarks, results in
models designated as type-XII2HDMVLQ. Additionally, we have explored double
Higgs production within this model and observed when both the heavy Higgs and
VLQ contribute the double Higgs production cross section significantly
enhanced.
