According to the interesting comment of Mohammad F Tehrani, I revise the question as follows:

Assume $n>2$. For what type of compact n dimensional manifolds $M$ we can say:

For every smooth embedding $f:M \to \mathbb{R}^{2n}$, there exist a point $p \in M$such that $Df_{p}(T_{p} M)$ is a lagrangian subspace of $R^{2n}$?

Is there an example of a manifold with this property? For example: does $S^{3}$ satisfy this property?