What is the method for making up for the past days of Shawwal fasting from previous years, the number of which has not been determined, and is it permissible to pay expiation instead of fasting them?

The correct view, according to the majority of jurists, is that it is not permissible to combine intentions for fasting. As for the issue of whether fasting the six days of Shawwal can count for making up missed fasts (qada') or for the supererogatory six days, there are three opinions: it counts for qada', it counts for the supererogatory, or it counts for neither. The preferred opinion is that it counts for qada', supported by the fatwa of Imam Al-Ramli.