In this work, we explore the application of multilinear algebra in reducing the order of multilinear time-invariant (MLTI) systems. We use tensor Krylov subspace methods as key tools, which involve approximating the system solution within a low-dimensional subspace. We introduce the tensor extended block and global Krylov subspaces and the corresponding Arnoldi based processes. Using these methods, we develop a model reduction method using projection techniques. We also demonstrate how these methods can be used to solve large-scale Lyapunov tensor equations, which are essential for the balanced truncation method, a technique for order reduction. We show how to extract approximate solutions via the Einstein product using the tensor extended block Arnoldi and the extended global Arnoldi processes.