This paper reports the result of a search for the standard model Higgs boson in events containing four reconstructed jets associated with quarks. For masses below 135 GeV/c 2, the Higgs boson decays to bottom-antibottom quark pairs are dominant and result primarily in two hadronic jets. An additional two jets can be produced in the hadronic decay of a W or Z boson produced in association with the Higgs boson, or from the incoming quarks that produced the Higgs boson through the vector-boson fusion process. The search is performed using a sample of √s=1.96 TeV proton-antiproton collisions corresponding to an integrated luminosity of 9.45 fb−1 recorded by the CDF II detector. The data are in agreement with the background model and 95% credibility level upper limits on Higgs boson production are set as a function of the Higgs boson mass. The median expected (observed) limit for a 125 GeV/c 2 Higgs boson is 11.0 (9.0) times the predicted standard model rate.