  In the context of observed massive neutron stars (NSs), we examine the
internal structure, phase transitions, and the impacts of the equation of state
(EOS) in maximum NSs. We investigate the stiffness changes in the EOS during
the hadron-quark phase transition within the NSs. The relativistic mean-field
(RMF) model and RMF model with a density-dependent isovector coupling, known as
the RMFL model, are used to describe hadronic matter, while to the represent
quark matter, the Nambu-Jona-Lasinio (NJL) model is applied. We explore the
strength of vector coupling in quark matter, which delayed the onset density
and reduced the maximum mass of NS, but does not exhibit a clear correlation
with the NS central density. A considerable size of the mixed phase core could
exist in the maximum mass NS but with corresponding small mixed phase mass.
