We present a measurement of the top-quark mass Mtop in the all-hadronic decay channel tt→W+bW−b→q1q2bq3q4b. The analysis is performed using 310  pb−1 of s√=1.96  TeV pp collisions collected with the CDF II detector using a multijet trigger. The mass measurement is based on an event-by-event likelihood which depends on both the sample purity and the value of the top-quark mass, using 90 possible jet-to-parton assignments in the six-jet final state. The joint likelihood of 290 selected events yields a value of Mtop=177.1±4.9(stat)±4.7(syst)  GeV/c2.