Demonstrate your understanding of Python file handling by completing the following tasks.
Tasks:
File Creation: Create a Python script (file_handling_assignment.py) that does the following: Creates a new text file named "my_file.txt" in write mode ('w'). Write at least three lines of text to the file, including a mix of strings and numbers.
File Reading and Display: Enhance your script to read the contents of "my_file.txt" and display them on the console.
File Appending: Modify the script to open "my_file.txt" in append mode ('a'). Append three additional lines of text to the existing content.
Error Handling: Implement error handling using try, except, and finally blocks to manage potential file-related exceptions (e.g., FileNotFoundError, PermissionError).