  This paper investigates the necessary and sufficient algebraic conditions to
a constrained system of Sylvester-type quaternion tensor equations. An explicit
formula of the general solution regarding the Moore-Penrose inverses of some
block given tensors is obtained. As an application of a particular case, we
establish the solvability conditions and the general solution to a system of
Sylvester-type quaternion tensor equations involving $\eta$-Hermitian unknowns.
An algorithm with a numerical example is proposed to compute the general
solution of the main system.
