Unraveling the physics of nonlinearly excited spin waves provides a powerful platform for understanding analogous physical phenomena governed by universal nonlinear equations. While the excitation and detection of nonlinear spin waves have been widely demonstrated, the precise physical mechanisms governing their generation and exact spectral characteristics remain poorly understood. Bridging this fundamental gap is essential for harnessing nonlinear magnonic phenomena and rationally designing advanced spin-wave devices. Here, we comprehensively investigate spin-wave excitations in Permalloy nanowires utilizing a highly sensitive, selectively modulated electrical detection scheme for probing spin dynamics. Above a threshold microwave power, we observe a distinct, discrete secondary spin-wave resonance. Kinematic analysis reveals that transverse spatial confinement enables multi-path inter-mode four-magnon scattering, whose simultaneously available pathways expand the phase space under specific kinematic conditions. Micromagnetic simulations corroborate that these pathways can be activated simultaneously and give rise to a secondary resonance peak. Based on this combined experimental and numerical evidence, we attribute the observed secondary resonance to this multi-path scattering mechanism.