  Using data collected by the FOCUS experiment at Fermilab, we report the
discovery of the decay modes D^0 --> K- pi+ pi+ pi+ pi- pi- and D^0 --> pi+ pi+
pi+ pi- pi- pi-. With a sample of 48 +/- 10 reconstructed D^0 --> K- pi+ pi+
pi+ pi- pi- decays and 149 +/- 17 reconstructed D^0 --> pi+ pi+ pi+ pi- pi- pi-
decays, we measure the following relative branching ratios:
  ${\Gamma (D^0 \to K^- \pi^+ \pi^+ \pi^+ \pi^- \pi^-) / \Gamma (D^0 \to K^-
\pi^+ \pi^+ \pi^-)} = (2.70 \pm 0.58 \pm 0.38) \times 10^{-3}$
  ${\Gamma (D^0 \to \pi^+ \pi^+ \pi^+ \pi^- \pi^- \pi^-) / \Gamma (D^0 \to K^-
\pi^+ \pi^+ \pi^-)} = (5.23 \pm 0.59 \pm 1.35) \times 10^{-3}$
  ${\Gamma (D^0 \to \pi^+ \pi^+ \pi^+ \pi^- \pi^- \pi^-) / \Gamma (D^0 \to K^-
\pi^+ \pi^+ \pi^+ \pi^- \pi^-)} = 1.93 \pm 0.47 \pm 0.48$
  The first errors are statistical and the second are systematic. The branching
fraction of the Cabibbo suppressed six-body decay mode is measured to be a
factor of two higher than the branching fraction of the Cabibbo favored
six-body decay mode.
