This paper investigates the solvability conditions and general solutions for the dual quaternion matrix equation \(AXB = C\). The authors provide necessary and sufficient conditions for the solvability of the equation and derive the general solution when these conditions are met. They also explore special cases of the equation, such as the \(\phi\)-Hermitian solutions to the equation \(AXA^\phi = C\), where \(\phi\) is a nonstandard involution. The paper includes a numerical example to illustrate the main results and discusses the broader applications of the matrix equation in various fields, including control theory, computer graphics, and mechanics.This paper investigates the solvability conditions and general solutions for the dual quaternion matrix equation \(AXB = C\). The authors provide necessary and sufficient conditions for the solvability of the equation and derive the general solution when these conditions are met. They also explore special cases of the equation, such as the \(\phi\)-Hermitian solutions to the equation \(AXA^\phi = C\), where \(\phi\) is a nonstandard involution. The paper includes a numerical example to illustrate the main results and discusses the broader applications of the matrix equation in various fields, including control theory, computer graphics, and mechanics.