**Core Concept:** Hypothyroidism is a disorder of the thyroid gland, characterized by low levels of thyroid hormones. Low TSH (thyroid-stimulating hormone) and low free T4 levels are indicative of hypothyroidism.

**Why the Correct Answer is Right:**
The correct answer is Option D (evaluate for Hashimoto's thyroiditis). Hashimoto's thyroiditis is a common cause of hypothyroidism, where the immune system attacks the thyroid gland, leading to reduced hormone production. In this case, the patient presents with symptoms of hypothyroidism, such as fatigue, constipation, alopecia, and weight gain. The elevated TSH (20 mU/L) and low free T4 levels indicate hypothyroidism.

**Why Each Wrong Option is Incorrect:**
A. Evaluate for autoimmune disorders (Hashimoto's thyroiditis is an autoimmune disorder causing hypothyroidism, making it the right choice)
B. Evaluate for nutritional deficiencies (hypothyroidism is caused by autoimmune disorders like Hashimoto's thyroiditis, not nutritional deficiencies)
C. Evaluate for medication side effects (Hashimoto's thyroiditis is an autoimmune disorder, not a medication side effect)
D. Evaluate for thyroid cancer (Hashimoto's thyroiditis is an autoimmune disorder causing hypothyroidism, making it the right choice)

**Clinical Pearl:** Hashimoto's thyroiditis is the most common cause of primary hypothyroidism. It is an autoimmune disorder where the body's immune system attacks the thyroid gland, leading to reduced hormone production. It is important to consider Hashimoto's thyroiditis for patients presenting with hypothyroidism symptoms, as it is the most common cause, and evaluating for other causes is unnecessary unless there are specific clinical findings or additional symptoms.

**Correct Answer:** D. Evaluate for Hashimoto's thyroiditis