This study investigates a planar hybrid system consisting of three complementary splitring resonators (CSRRs), designed to examine interactions among multiple photon modes at room temperature. The system was modeled and simulated using the full-wave electromagnetic solver CST Microwave Studio. Analysis of the transmission spectra (|S21|) as a function of frequency for different CSRR dimensions revealed distinct anti-crossing behavior, indicative of strong photon-photon coupling (PPC). To explain this phenomenon, we present theoretical framework that quantitatively captures the observed mode hybridization and provides estimates of the coupling strength, which are further validated experimentally. This work not only elucidates the fundamental dynamics of PPC in planar systems but also offers practical guidance for designing hybrid platforms with tunable photon interactions, paving the way for future advancements in planar magnonic and hybrid photonic technologies.