In Python, the `extend()` method is used to append all the elements of a list to another list. Let's examine each option:
Option (A): `A.extend(B)` will add all elements of list \( B \) to list \( A \), resulting in \( A = [1, 2, 3, 4, 5, 6] \). This is the correct answer.
Option (B): `A.append(B)` will add list \( B \) as a single element to list \( A \), resulting in \( A = [1, 2, 3, [4, 5, 6]] \), which is incorrect.
Option (C): There is no `update()` method for lists in Python, so this is incorrect.
Option (D): `A.insert(B)` is used to insert an element at a specific index, and it cannot be used with an entire list like \( B \). This is also incorrect.
Thus, the correct answer is Option (A), which uses `A.extend(B)`.