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Hybrid magnonics, exploring the coupling between magnons and quantum systems, is an exciting field for developing next-generation information technologies. Achieving a strong and tunable magnon-magnon coupling (MMC) in confined nanomagnets is crucial for the on-chip integration of these hybrid systems and advancing the field. In this work, we numerically investigate the interactions between different magnon modes excited within an elliptical magnonic nano-disc (EMND), demonstrating an anti-crossing effect in the dispersion spectra. A comprehensive theoretical framework was presented that explains this anti-crossing phenomenon as a result of MMC and provide estimates for the strength of the coupling (g). Furthermore, we show that this intermodal coupling can be tuned from a strong coupling regime (g = 300 MHz) to a weak coupling regime by varying the direction of the external magnetic field and the intrinsic properties of the EMND. Our combined numerical and theoretical findings offer new insights into MMC, significantly advancing the field of quantum magnonics and magnon-based quantum information technology., Comment: 24 pages, 5 figures, to be published in Journal of Applied Physics