Studying fluid dynamics is crucial to advancing scientific knowledge and technological advancements worldwide. This study examines the behavior of a viscous fluid when it interacts with two horizontally positioned rectangular polygons arranged in a staggered arrangement. The lattice Boltzmann method is employed to analyze two-dimensional flow, specifically focusing on two physical parameters: Reynolds number, which is fixed at 150, and gap spacings, which vary simultaneously in X and Y directions. The results are analyzed by examining vortex snapshots, time trace histories of drag and lift coefficients, and power spectra analysis of lift coefficients. The progressive increase in the gap distances between the two horizontal rectangular polygons distinguishes seven separate flow vortex streets. The vortex shedding mechanism is disrupted at narrow gap spacings and reaches its ideal state at large gap spacings. There is the potential for the flow regime to be altered by the staggered alignment of rectangular polygons. Increasing the space between the polygons has a considerable impact on the flow characteristics brought about.