You must make up your missed fasts from Ramadan before offering Shawwal fasts. It does not have to be in consecutive order.
Kindly refer to the following link(s):
Can we combine the 6 days of shawwal with the missed fasts of Ramadan?
Can we Combine 6 days of shawwal with the missed Ramadan Fast? | By Assim Al Hakeem
Should I first make up the missed days of Ramadan before 6 days of Shawwal?