Now, first is the root directory. S$1,$ S$2,$ and S$3$ are mounted under the $"/$user$/$dir$1/$local$"$ directory.

Under S$1,$ there is a "library" directory, and under that, an "economics" directory. This path is valid.

Under S$2,$ there is a "library$1"$ directory, and under that, an "engineering" directory. This path is also valid.

Under S$3,$ there is a "local$1"$ directory, and under that, a "library$2"$ directory. This path is valid as well.

Now, let's see whether S$4$ can be mounted or not. S$4$:$/$user$/$S$3/$economics implies that S$3$ is mounted under $"/$user$/$S$3"$ directory. But in

the file structure, there is no $"$S$3"$ directory, so this mounting is not possible.