Step 1: Anchor on the cell of origin. Medullary thyroid carcinoma is a neuroendocrine tumor of the calcitonin-secreting parafollicular C cells, which are derived from the neural crest, unlike the follicular epithelium that gives rise to most thyroid cancers.
Step 2: RET is a growth-factor receptor that is physiologically active in these neural crest lineages, including the thyroid C cells and adrenal medulla. A constitutively activating mutation therefore transforms exactly these cells.
Step 3: This explains why RET sits at the centre of the MEN-2 syndromes (2A and 2B) and familial MTC, where medullary thyroid cancer is the common thread alongside pheochromocytoma.
Step 4: Eliminate the rest: a glial-origin astrocytoma, a SDH-linked paraganglioma, and a follicular-derived Hurthle cell tumor all lie outside the RET pathway. The single best fit is medullary thyroid carcinoma.
\[\boxed{\text{Medullary carcinoma thyroid}}\]