Short Answer

It is highly recommended to fast any six days, besides the day of Eid, in Shawwāl. It does not have to be in order. You normally must not perform a random optional fast before making up missed fasts from Ramadan. However, if the optional fast is time-bound, then you can do it (like the six of Shawwāl, Arafah, or Ashūrā) before making up a missed fast from Ramadan because it is technically not a requirement to make up those days immediately, but rather by the following Ramadan.

Version 0.25

Shaykh Mustafa Umar