Here it is just inserting a new node $N$ in right of $M$.
as it is a Doubly Linked List , so it has two pointers , one pointing to the previous node $(Lptr)$ and the other point to the next node$(Rptr)$.
in this case ,
$N → lptr = M ;$
The previous pointer of $N$ is pointed to $M$.
$N → rtptr = M → rptr ;$
Now, the next pointer of $N$ is pointed to that node to which the next pointer of $M$ was pointing .
$N → lptr → rptr = N ;$
The next pointer of $M$ is pointing to $N$ ( as the previous pointer of $N$ is nothing but $M$)
$N → rptr → lptr = N ;$
The , previous pointer of next node of $N$ is now pointing to $N$.