We present a measurement of the top-quark mass, $M_{\mathrm{top}}$, in the all-hadronic decay channel $t\bar{t} \to W^+b W^- \bar{b} \to q_1\bar{q}_2 b q_3 \bar{q}_4 \bar{b}$. The analysis is performed using 310 pb$^{-1}$ of $\sqrt{s}$=1.96 TeV $p\bar{p}$ collisions collected with the CDF II detector using a multi-jet 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 $M_{\mathrm{top}}$=177.1 $±$ 4.9 (stat.) $±$ 4.7 (syst.) GeV/$c^2$. ; Comment: 7 pages, 2 figures and 1 table, Submitted to Phys. Rev. Lett