Assuming the SectionPages field in Section 3 is marked with a bookmark named Sec3Pages, the formula for the footer page number for Section 4 would be:
{ = { Page } - { Sec3Pages } }

The field code display is toggled on and off using Alt-F9. This is a global setting and applies to all documents in Word until toggled on or off.

Remember that the braces {} must be entered using the Insert Field command or Ctrl-F9. You cannot just type them using the keyboard.