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 s√=1.96  TeV and corresponds to an integrated luminosity of 8.7  fb−1.