This article reports results of experimental investigation of the spin wave interference over large distances in the Y3Fe2(FeO4)3 waveguide using Brillouin-Mandelstam spectroscopy. Two coherent spin waves are excited by the micro-antennas fabricated at the edges of the waveguide. The amplitudes of the input spin waves are adjusted to provide approximately the same intensity in the central region of the waveguide. The relative phase between the excited spin waves is controlled by the phase shifter. The change of the local intensity distribution in the standing spin wave is monitored using Brillouin-Mandelstam light scattering spectroscopy. Experimental data demonstrate the oscillation of the scattered light intensity depending on the relative phase of the interfering spin waves. The oscillations of the intensity, tunable via the relative phase shift, are observed as far as 7.5 mm away from the spin-wave generating antennas at room temperature. The obtained results are important for developing techniques for remote control of spin currents, with potential applications in spin-based memory and logic devices.