We use a sample of diphoton + dijet events to measure the effective cross section of double parton interactions, which characterizes the area containing the interacting partons in proton-antiproton collisions, and find it to be σeff = 19.3 ± 1.4(stat) ± 7.8(syst) mb. The sample was collected by the D0 detector at the Fermilab Tevatron collider in pp collisions at [?] = 1.96 TeV and corresponds to an integrated luminosity of 8.7 fb-1