Step 1: A thyroglossal duct anomaly arises from the embryological tract along which the thyroid descends from the tongue base to the neck. The lesion may present as a midline cyst or, after infection and rupture, as a fistula.
Step 2: Both presentations are managed surgically by the Sistrunk technique, which removes the cyst or sinus together with the central body of the hyoid bone and the remaining tract up to the foramen cecum.
Step 3: Because the operation addresses both the cystic and the fistulous forms of the same condition, options b and c are each valid answers.
Step 4: The parotid choice is unrelated and is handled by parotidectomy, so the combined option covering both b and c is correct.
\[\boxed{\text{Both thyroglossal fistula and thyroglossal cyst}}\]