Using 818 pb[-]1 of e+ e[-] collisions recorded at the psi resonance with the CLEO-c detector at CESR, we determine absolute hadronic branching fractions of charged and neutral D mesons using a double tag technique. Among measurements for three D0 and six D+ modes, we obtain reference branching fractions B(D0 [RIGHTWARDS ARROW] K [-] [pi]+ ) = (3.906 ± 0.021 ± 0.062)% and B(D+ [RIGHTWARDS ARROW] K [-] [pi]+ [pi]+ ) = (9.157 ± 0.059 ± 0.125)%, where the first uncertainty is statistical, the second is systematic errors. Using an independent determination of the integrated luminosity, we also extract the cross sections [sigma](e+ e[-] [RIGHTWARDS ARROW] D0 D0 ) = (3.650 ± 0.017 ± 0.083) nb and [sigma](e+ e[-] [RIGHTWARDS ARROW] D+ D[-] ) = (2.920 ± 0.018 ± 0.062) nb at a center of mass energy, Ecm = 3774 ± 1 MeV.