In this paper, we introduce the definition of the generalized reduced
biquaternions and propose a real representation of a generalized reduced
biquaternion matrix. By using the matrix representation, we discuss the
least-squares problems of the classic generalized reduced biquaternion
matrix equation $AXC=B$. The least-squares solution to the above
matrix equation is formulated by a least-squares real solution of its
corresponding real matrix equation. Furthermore, two numerical examples
are given to illustrate our results.