Distance-biregular graphs form a natural bipartite generalization of distance-regular graphs. Among them, the class of 2-Y-homogeneous distance-biregular graphs plays a prominent role and has been the subject of several recent classification efforts. In this paper, we complete the classification of 2-Y-homogeneous \((Y,Y')\) -distance-biregular graphs with eccentricity \(D=4\) . Building on earlier work that settled the cases \(c_2'=1\) and \(c_2'=2\) , we address the remaining open case \(c_2'\ge 3\) . We prove that no such graphs exist, thereby resolving an open problem posed in previous work and closing the classification program for eccentricity \(D=4\) . Our approach combines a detailed analysis of intersection numbers, arithmetic constraints arising from 2-Y-homogeneity, and structural properties of distance-biregular graphs. As a consequence, we obtain a complete characterization of all 2-Y-homogeneous distance-biregular graphs with \(D=4\) , and we further conclude that every 2-Y-homogeneous distance-biregular graph with \(c_2'\ge 3\) must necessarily have eccentricity \(D=3\) .
