  The reaction mechanisms of the two-neutron transfer reaction
$^{12}$C($^6$He,$^4$He) have been studied at 30 MeV at the TRIUMF ISAC-II
facility using the SHARC charged-particle detector array. Optical potential
parameters have been extracted from the analysis of the elastic scattering
angular distribution. The new potential has been applied to the study of the
transfer angular distribution to the 2$^+_2$ 8.32 MeV state in $^{14}$C, using
a realistic 3-body $^6$He model and advanced shell model calculations for the
carbon structure, allowing to calculate the relative contributions of the
simultaneous and sequential two-neutron transfer. The reaction model provides a
good description of the 30 MeV data set and shows that the simultaneous process
is the dominant transfer mechanism. Sensitivity tests of optical potential
parameters show that the final results can be considerably affected by the
choice of optical potentials. A reanalysis of data measured previously at 18
MeV however, is not as well described by the same reaction model, suggesting
that one needs to include higher order effects in the reaction mechanism.
