The vector-boson production cross section for the Higgs boson decay in the Formula Presented channel is measured as a function of kinematic observables sensitive to the Higgs boson production and decay properties as well as integrated in a fiducial phase space. The analysis is performed using the proton-proton collision data collected by the ATLAS detector in Run 2 of the LHC at Formula Presented center-of-mass energy, corresponding to an integrated luminosity of Formula Presented. The different flavor final state is studied by selecting an electron and a muon originating from a pair of Formula Presented bosons and compatible with the Higgs boson decay. The data are corrected for the effects of detector inefficiency and resolution, and the measurements are compared with different state-of-the-art theoretical predictions. The differential cross sections are used to constrain anomalous interactions described by dimension-six operators in an effective field theory.