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The results of the analysis of the new experimental astrophysical S factors Sexp24(E) [D. Trezzi et al., Astropart. Phys. 89, 57 (2017)] and those measured earlier [R. G. Robertson et al., Phys. Rev. Lett. 47, 1867 (1981)] for the nuclear-astrophysical d(α,γ)6Li reaction directly measured at extremely low energies E, which is derived within the modified two-body potential method, are presented. New estimates and their uncertainties have been obtained for values of the asymptotic normalization coefficient for α+d→6Li and for the direct astrophysical S factors at Big Bang energies.