Python - Downloading map tiles
Cool python exercise! And a nice job.
I'm going to assume you are using python3. There are some points of improvement:


Multiline strings: In python you can create a string with more than one line using """ so you an put all of the printing in the beginning of your program in one print statement.
Pathlib: There is a library called pathlib which allows you to create multi platform path objects. Try to use it instead of concatenating strings yourself.
Constants in capitals: Is access_rights a constant? Write it in capital letters if so (It's a normal naming convention).
String formatting: You can use fstrings instead of format, it looks much nicer and more readable (to me). So "Downloading images to {}{}.".format(path,x) can now be f"Downloading images to {path}{x}.".
List comprehension: you can create the yz_array using list comprehension, it is a bit complicated but it will look like: [2 ** x for x in range(8)] - will get the same result!
Meaningful variable names: instead of x even use x_index.
Meaningful exceptions: Using Exception as e you can print the system error, giving the user more information.
Logical error: Notice that even if there was an error in the file creation process you will still print "Successfully filled folder" which is not true. Add a boolean variable to prevent that.
Multi Platform compatibility: You are probably using windows, but on other os your code will crush, by adding another try - catch you can prevent that. You can also try and find the os and create a matching case for windows.


Maybe:


Functions: You can use functions to avoid the indentations.
Spaces: According to PEP8 you should add a space after a , and you should not add space after a print statement.
Use type annotation: (Last but this one is my personal favourite) When your code gets complicated and you start to use function - Do not forget to read about type annotations.


Overall - greate code, nicely written.
Good luck and Have fun!