Step 1: Understanding the Concept:
A multinodular goitre grows slowly over years, usually from low iodine intake or long term thyroid stimulating hormone drive. The question asks which cancer tends to develop inside such a gland.
Step 2: Key Formula or Approach:
Match each thyroid cancer to its classic trigger: papillary to radiation, medullary to MEN syndromes and C cells, anaplastic to very old age, and follicular to iodine deficient, longstanding multinodular glands.
Step 3: Detailed Explanation:
In regions with low dietary iodine, the thyroid enlarges over years into a multinodular gland as it works harder to trap iodine.
Within this chronic setting, follicular cells can undergo malignant change, giving rise to follicular carcinoma, which is well described as arising from longstanding multinodular goitre.
Papillary carcinoma, by contrast, is the most common thyroid cancer in general and is tied more to prior radiation exposure than to iodine deficient goitre.
Medullary carcinoma comes from C cells and often runs in families as part of MEN 2, unrelated to goitre duration.
Anaplastic carcinoma is rare and aggressive, seen mostly in elderly patients, and though it can follow a longstanding goitre, it is not the classic textbook pairing being tested here.
Step 4: Final Answer:
The cancer classically arising from a longstanding multinodular goitre is follicular carcinoma.
\[ \boxed{\text{Follicular carcinoma}} \]