I have difficulties to understand the hierarchical notation of turing machine which is shown in the attached photo. Note that this is not assignment , it is already question and solution in the book but i didn't understand the solution. Please tell me the solution step by step , i didn't understand it.(i must understand it because it can be asked in final exam.) Or if you find and understand similar questions , you can explain it too.

Similar examples and the topic exist in the below links:

link
downloads .word
Any help is much appreciated.

turing-example.png