The Homotopy Types of Suspended Simply-connected $6$-manifolds

Under the assumption that certain Adem cohomology operation acts trivially on $H^2(M;\mathbb{Z}\mathrm{/}2)$, we determine the homotopy types of the triple suspension ${\mathrm{\Sigma }}^{3}M$ of a simply-connected oriented closed topological(or smooth) $6$-manifold $M$, whose integral homology groups can have $2$-torsion.