Dissociation of a 240 MeV/u beam of He-6, incident on carbon and lead targets, has been studied in kinematically complete experiments to investigate low-lying excitation modes in the halo nucleus He-6. It is shown that alignment effects characterize the inelastic scattering and allow an unambiguous assignment of the spin of a narrow resonance observed in the excitation energy spectrum. The differential cross sections for the He-6 inelastic scattering on carbon and lead targets were deduced from the measured moments of the two neutrons and the a-particle. An analysis of these distributions shows that quadrupole and, possibly, monopole excitations characterize the hadronic interaction, while the dipole mode is dominating in Coulomb dissociation. Neither theoretically predicted new resonance states in He-6 nor nuclear excitation of a dipole mode were found. Direct evidence has been obtained for strong suppression of Coulornb post-acceleration in direct Coulomb breakup in a lead target.