- The method \texttt{A.append(B)} treats the entire list \( B \) as a single element, leading to \([1,2,3,[4,5,6]]\), which is incorrect.
- The method \texttt{A.update(B)} is not applicable to Python lists, as it is used for sets and dictionaries.
- The method \texttt{A.insert(B)} is incorrect because \texttt{insert()} requires both an index and a value, making it unsuitable for concatenating lists.
- The correct approach is \texttt{A.extend(B)}, which adds each element of \( B \) individually to \( A \), resulting in \([1,2,3,4,5,6]\).
Conclusion:
The correct method is \texttt{A.extend(B)}, as it appends the individual elements of \( B \) to \( A \) rather than nesting the list.