**Core Concept:** Thyroid function testing involves measuring thyroid hormones and thyroid-stimulating hormone (TSH) levels to assess thyroid status. Thyroid peroxidase antibodies (TPOAb) are a marker of autoimmune thyroid disease.

**Why the Correct Answer is Right:** This patient presents with elevated TSH (6mIU/L) and low free T4 (12.4 pmol/L or 0.96 ng/dL) levels, suggesting primary hypothyroidism. Additionally, strongly positive TPOAb indicates an autoimmune process. Levothyroxine therapy is indicated in primary hypothyroidism, which is the case here, as the patient's mother is already on levothyroxine, and her thyroid function tests (TFTs) are within normal range.

**Why Each Wrong Option is Incorrect:**

A. **Incorrect answer**: Normal thyroid function tests (TFTs) would indicate no treatment is needed, as the patient's thyroid status does not align with the observed symptoms and family history.

B. **Incorrect answer**: Low TSH levels (0.1-4.0 mIU/L) indicate hyperthyroidism, which is not consistent with the patient's symptoms, family history, and elevated TSH levels.

C. **Incorrect answer**: Strongly positive TPOAb is a marker of autoimmune thyroid disease, but does not directly dictate treatment initiation. The patient also presents with clinical features and family history of hypothyroidism, which warrants levothyroxine therapy.

D. **Incorrect answer**: Normal TPOAb levels would not support the diagnosis of autoimmune thyroid disease, which is indicated by the patient's clinical presentation and family history.

**Clinical Pearl:** Strongly positive TPOAb, along with clinical features of hypothyroidism and a family history of levothyroxine treatment, strongly indicates autoimmune thyroid disease (Hashimoto's thyroiditis). Management typically involves initiating levothyroxine therapy to replace the deficient thyroid hormone.

**Correct Answer:**

**Correct Answer:** D. Levothyroxine therapy is necessary to treat the patient's primary hypothyroidism due to autoimmune thyroid disease, indicated by elevated TSH levels and strongly positive TPOAb. Initiating levothyroxine therapy aligns with the patient's clinical presentation and family history of treatment.