We present a measurement of the top-quark mass using a sample of tt events in 5.7  fb−1 of integrated luminosity from pp collisions at the Fermilab Tevatron with s√=1.96  TeV and collected by the CDF II Detector. We select events having large missing transverse energy, and four, five, or six jets with at least one jet tagged as coming from a b quark, and reject events with identified charged leptons. This analysis considers events from the semileptonic tt decay channel, including events that contain tau leptons. The measurement is based on a multidimensional template method. We fit the data to signal templates of varying top-quark masses and background templates, and measure a top-quark mass of Mtop=172.32±2.4(stat)±1.0(syst)  GeV/c2.