  This paper presents an efficient method for obtaining the least squares
Hermitian solutions of the reduced biquaternion matrix equation $(AXB, CXD) =
(E, F )$. The method leverages the real representation of reduced biquaternion
matrices. Furthermore, we establish the necessary and sufficient conditions for
the existence and uniqueness of the Hermitian solution, along with a general
expression for it. Notably, this approach differs from the one previously
developed by Yuan et al. $(2020)$, which relied on the complex representation
of reduced biquaternion matrices. In contrast, our method exclusively employs
real matrices and utilizes real arithmetic operations, resulting in enhanced
efficiency. We also apply our developed framework to find the Hermitian
solutions for the complex matrix equation $(AXB, CXD) = (E, F )$, expanding its
utility in addressing inverse problems. Specifically, we investigate its
effectiveness in addressing partially described inverse eigenvalue problems.
Finally, we provide numerical examples to demonstrate the effectiveness of our
method and its superiority over the existing approach.
