We demonstrate the coexisting four-wave mixing (FWM) signal and six-wave mixing (SWM) signal which can be enhanced both by electromagnetically induced transparency (EIT) and optical pumping effect in a common three-level and open four-level inverted-Y type systems of 85Rb. We also analyze the effect of optical pumping in different energy level systems by arranging laser beams and comparing the strength of the increased and reduced absorption caused by optical pumping.