Evidence for a flavor asymmetry between the ū and d¯ quark distributions in the proton has been found in deep-inelastic scattering and Drell-Yan experiments. The pronounced dependence of this flavor asymmetry on x (fraction of nucleon momentum carried by partons) observed in the Fermilab E866 Drell-Yan experiment suggested a drop of the d¯(x)/ū(x) ratio in the x>0.15 region. We report results from the SeaQuest Fermilab E906 experiment with improved statistical precision for d¯(x)/ū(x) in the large x region up to x=0.45 using the 120 GeV proton beam. Two different methods for extracting the Drell-Yan cross section ratios, σpd/2σpp, from the SeaQuest data give consistent results. The d¯(x)/ū(x) ratios and the d¯(x)-ū(x) differences are deduced from these cross section ratios for 0.13