  Within the framework of the theory of quaternion column-row determinants and
using determinantal representations of the Moore-Penrose inverse previously
obtained by the author, we get explicit determinantal representation formulas
of solutions (analogs of Cramer's rule) to the quaternion two-sided generalized
Sylvester matrix equation $ {\bf A}_{1}{\bf X}_{1}{\bf B}_{1}+ {\bf A}_{2}{\bf
X}_{2}{\bf B}_{2}={\bf C}$ and its all special cases when its first term or
both terms are one-sided. Finally, we derive determinantal representations of
two like-Lyapunov equations.
