Is it possible to use had to + past participle?

Solution 1:

Your teacher made a mistake. "She had to took over" is incorrect grammar.

Solution 2:

In fact, "took" is the past simple of "take", and "taken" is the past participle. It is highly unlikely that a teacher should confuse "take" and "took". I wonder whether your teacher merely crossed out only part ("take") of what she actually meant to cross out ("had to take over") in order to have "after the death of her grandfather, she took over his duties on the farm."

"Had to" (and "have to" in any tense) has to be followed by infinitive.

She had to take over.

I had to do that.

I have to go.

I will have to wait.