The paper proves that all general smooth Fano threefolds of Picard rank 3 and degree 14 are K-stable. The authors show that a general smooth Fano threefold with these properties is K-stable, and that if the discriminant curve of the conic bundle structure is smooth, then the threefold is K-stable. They also show that if the singular fibers of the del Pezzo fibrations have singular points of types $A_1$ and $A_2$, then the threefold is K-stable. The proof involves analyzing the geometry of the Fano threefold, its del Pezzo surfaces, and using Abban-Zhuang theory to compute invariants that determine K-stability. The authors also consider the case where the conic bundle has multiple fibers and show that under certain conditions, the threefold remains K-stable. The main result is that under the given generality condition, the Fano threefold is K-stable.The paper proves that all general smooth Fano threefolds of Picard rank 3 and degree 14 are K-stable. The authors show that a general smooth Fano threefold with these properties is K-stable, and that if the discriminant curve of the conic bundle structure is smooth, then the threefold is K-stable. They also show that if the singular fibers of the del Pezzo fibrations have singular points of types $A_1$ and $A_2$, then the threefold is K-stable. The proof involves analyzing the geometry of the Fano threefold, its del Pezzo surfaces, and using Abban-Zhuang theory to compute invariants that determine K-stability. The authors also consider the case where the conic bundle has multiple fibers and show that under certain conditions, the threefold remains K-stable. The main result is that under the given generality condition, the Fano threefold is K-stable.