Working from the inside out, this formula first concatenates the last name in column C with the first letter of the first name from column B:
The LEFT function is normally configured with num_chars, but the argument is optional and left will extract 1 character from the left when it is absent. This results in the text string "atanaka".
Next, the domain name is added like this:
Note that the reference to the domain name is absolute ($G$6) so that the formula can be copied down the table without this reference changing.
Finally, the lower function is used to lowercase the entire string:
which returns a final result of "email@example.com"