This research activity focuses on developing efficient preconditioned iterative solvers for solving Sylvester tensor equations. By leveraging the structure of the tensor equation, a novel projection method is proposed to improve the convergence rate of the solvers. The method exploits the Kronecker product structure of the tensor equation, leading to a significant reduction in computational complexity. The goal is to provide a robust and efficient solution for solving Sylvester tensor equations, with applications in various fields such as signal processing and machine learning.