Final answer:
Medullary thyroid carcinoma is the type of thyroid cancer that originates from the parafollicular C-cells in the thyroid gland that produce the hormone calcitonin.
Step-by-step explanation:
The type of thyroid cancer that arises from parafollicular C-cells is called medullary thyroid carcinoma (MTC). The parafollicular C-cells in the thyroid gland produce the hormone calcitonin, which is involved in regulating calcium levels in the blood. When these cells turn cancerous, they can lead to MTC, a rare and distinct form of thyroid cancer that is different from cancers arising from thyroid follicular cells.