  The low energy effective theory ($\sim$ TeV) of the little-Higgs model with
$SU(6)/Sp(6)$, as proposed by Low, Skiba and Smith (LSS), exhibits a two-Higgs
doublet model (2HDM) structure. The symmetry dictates interesting Yukawa
patterns, translating to non-trivial fermion couplings with both of the Higgs
doublets. The couplings of the scalars with the fermions can induce flavor
changing neutral currents (FCNC), which get constraints from flavor physics
observables such as BR$(B\rightarrow X_s\gamma)$, $B_s - \bar{B}_s$ mixing etc.
The precision measurement of $Z b \bar{b}$ vertex, the top and Higgs mass along
with other Higgs coupling measurements at the Large Hadron Collider (LHC) also
enforce severe restrictions on the LSS model. Direct LHC search results of
beyond the Standard Model (BSM) particles also impose bounds on the masses. We
probe the LSS model in view of the above constraints through a random scan in
the multi-dimensional parameter space. We observe, on contrary to the general
2HDM scenario, the emergent 2HDM from the LSS model is less constrained from
the flavor data and the $Z b \bar{b}$ measurement but is severely constrained
form the electroweak (EW) searches at the LHC. From the flavor data and $Z b
\bar{b}$, we find that the charged Higgs mass is relaxed with $\tan\beta$ being
restricted to $0.5-5$, whereas the charged Higgs mass is pushed to larger than
1 TeV along with $\tan\beta$ being further restricted to $< 3$ when the LHC
bounds are incorporated.
