Position in the Linked-list
First of all, let me strongly recommend avoiding outdated textbooks such as Aho, Hopcroft and Ullman.
Let me also replace Aho, Hopcroft and Ullman's use of &quot;position&quot; with the more common notion of pointer. In a linked list, each cell consists of a value and pointer to the following cell (if any). The linked list itself is represented as a pointer to its first cell (if any). Therefore, if we consider the list $a,b,c$, then a pointer which is pointing at the third element will be pointing at the cell containing $c$.
(This is also a good place to mention that unless you're programming in Fortran or in Excel, then your arrays are zero-based; that is, the first element is element number 0.)
Now suppose that $p$ is a pointer which currently points at the cell containing $c$. If you insert $x$ between $a$ and $b$, then $p$ will still be pointing at $c$. However, $c$ is now the fourth element rather than the third element.
In contrast, if the list were implemented as an array, then $p$ will be a pointer to the third element of the array. Therefore, after inserting $x$ between $a$ and $b$, the pointer $p$ will be pointing at $b$.