We have measured the branching ratio of the three-body process in the nonmesonic weak decay of Lambda12C to be 0.29+/-0.13. This result was obtained by reproducing the nucleon and the nucleon pair yields introducing a measured final state interaction. At the same time, we have determined the absolute decay widths, Gamma(n) and Gamma(p), along with Gamma2N, whose relative ratio has been a long-standing puzzle. Including the three-body process, we have successfully reproduced the nucleon energy distribution, the coincidence two-nucleon angular correlation, and the momentum sum distribution simultaneously.