This paper investigates the solvability of the dual quaternion matrix equation $ AXB = C $ and provides the general solution when it is solvable. Dual quaternions, which extend real numbers and quaternions, have applications in various fields such as computer graphics, mechanics, and control theory. The study establishes necessary and sufficient conditions for the solvability of the equation using Moore–Penrose inverses and matrix ranks. It also introduces the concept of $ \phi $-Hermitian solutions, which generalize the ideas of Hermiticity and $ \eta $-Hermiticity. The paper derives the general solution for the equation and applies it to find $ \phi $-Hermitian solutions for a specific dual quaternion matrix equation $ AXA^{\phi} = C $. A numerical example is provided to illustrate the main results. The research contributes to the understanding of dual quaternion matrix equations and their applications in various mathematical and engineering contexts.This paper investigates the solvability of the dual quaternion matrix equation $ AXB = C $ and provides the general solution when it is solvable. Dual quaternions, which extend real numbers and quaternions, have applications in various fields such as computer graphics, mechanics, and control theory. The study establishes necessary and sufficient conditions for the solvability of the equation using Moore–Penrose inverses and matrix ranks. It also introduces the concept of $ \phi $-Hermitian solutions, which generalize the ideas of Hermiticity and $ \eta $-Hermiticity. The paper derives the general solution for the equation and applies it to find $ \phi $-Hermitian solutions for a specific dual quaternion matrix equation $ AXA^{\phi} = C $. A numerical example is provided to illustrate the main results. The research contributes to the understanding of dual quaternion matrix equations and their applications in various mathematical and engineering contexts.