My father died on 18th Ramadhaan while he was fasting and with 12 days remaining from the month. Is it incumbent upon me to make up for those 12 days on behalf of him? And in the case of it being so, then could I combine the intention of observing the six fasts of Shawwaal and the intention of making up for those days which my father did not fast, provided that I will complete the remaining days after finishing the six fasts of Shawwaal?
May Allaah reward you.

All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

We understand from your question that you ask about making up for the remaining fasts of Ramadan that your father did not catch, as he died before witnessing them. Being so, it should be known to you, may Allaah bless you, that these mentioned fasts are not due on your father because he died before witnessing them, and a dead person is addressed by no religious assignments, according to the consensus of  Muslims.

Consequently, it is impermissible to combine the intention of making up for the days your father did not fast with the intention of observing the six fasts of Shawwaal.

Allaah Knows best.