We employ classical molecular dynamics simulations to predict the experimentally validated dielectric spectra of a bulk 4-cyano-4'-hexylbiphenyl (6CB) system in the nematic phase at temperatures of 300 K and 290 K. We separately analyze the dielectric spectra parallel to the nematic director and perpendicular to it. They show different intensities and different relaxation times, with the parallel relaxation being slower (hundreds of nanoseconds) than the perpendicular (about 1 ns). We investigate various molecular motions as possible mechanisms for the observed macroscopic dielectric behavior by determining their characteristic time scales. We find that the parallel dielectric relaxation is realized by "head-over-heel" flips of 6CB molecules that invert their dipole moment. The perpendicular dielectric relaxation is traced to a combination of the precession of the long molecular axis (dipole axis) around the director and reorientations of the phenylene rings around the long-axis. Dihedral-angle transitions in the n-hexyl tails do not contribute to the dielectric signal.