We demonstrate efficient energy exchange during propagation between four-wave-mixing (FWM) and sixwave- mixing (SWM) signals generated in a four-level inverted-Y atomic system, which fall in the electromagnetically induced transparency window. AAfter an initial growth distance for both FWM and SWM fields in the atomic medium, these two nonlinear optical processes compete and exchange energy between them, and eventually reach their respective steady-state values at long interaction distance. A This energy exchange phenomenon can be explained by considering established atomic coherences among various atomic states and quantum interferences between three-photon and five-photon excitation pathways. A Understanding these highorder nonlinear optical processes and interplays between them can be very important for correlated FWM (or SWM) photon-pair generations and quantum information processing.