The extremely neutron-rich system 6H was studied in the direct 2H(8He, 4He) 6H transfer reaction with a 26A MeV secondary 8He beam. The measured missing mass spectrum shows a broad bump at ???4???8 MeV above the 3H +3n decay threshold. This bump can be interpreted as a broad resonant state in 6H at 6.8(5) MeV. The population cross section of such a presumably p-wave state (or it may be few overlapping states) in the energy range from 4 to 8 MeV is d??/d???c.m. ??? 190+40???80 ??b/sr in the angular range 5??? < ??c.m. < 16???. The obtained missing mass spectrum is practically free of 6H events below 3.5 MeV (d??/d???c.m. < 5 ??b/sr in the same angular range). The steep rise of the 6H missing mass spectrum at ???3 MeV allows us to derive the lower limit for the possible resonant-state energy in 6H to be 4.5(3) MeV. According to the paring energy estimates, such a 4.5(3) MeV resonance is a realistic candidate for the 6H ground state (g.s.). The obtained results confirm that the decay mechanism of the 7H g.s. (located at 2.2 MeV above the 3H+4n threshold) is the ???true??? (or simultaneous) 4n emission. The resonance energy profiles and the momentum distributions of fragments of the sequential 6H??? 5H(g.s.)+n??? 3H +3n decay were analyzed by the theoretically updated direct four-body-decay and sequential-emission mechanisms. The measured momentum distributions of the 3H fragments in the 6H rest frame indicate very strong ???dineutron-type??? correlations in the 5H ground state decay.