Here is the item again:
Because he had eaten a stack of twelve
pancakes,
(A) Emanuel
heard his stomach begin to rumble
(B) as it
processed the food. (C)
Gurgling loudly to protest the huge meal.
You correctly realized that the period after food created a fragment. Gurgling loudly to protest the huge meal is a participle phrase, which cannot stand alone as a complete sentence.
To fix this fragment, you chose to do this:
Because he had eaten a stack of twelve pancakes,
Emanuel heard his stomach begin to rumble as it processed the
food,
gurgling loudly to protest the huge meal.
You have correctly employed Punctuation Rule 3:
Main Clause + , + Participle Phrase.
Keep playing such beautiful music!