Step 1: Read the clinical picture. Fatigue with failure to gain weight (or weight loss despite appetite) and a warm body are classic features of a hypermetabolic state, that is, hyperthyroidism.
Step 2: Apply the feedback loop. In primary hyperthyroidism the thyroid overproduces T3 and T4. The high circulating thyroid hormone suppresses the pituitary, so TSH falls.
Step 3: Match the pattern. The expected result is therefore a low TSH with high T3 or T4, which is option A.
Step 4: Reject the others. A high TSH means hypothyroidism or subclinical hypothyroidism, which would cause weight gain and cold intolerance, the opposite of this patient. So the answer is low TSH with raised T3 or T4. Ref: Williams Textbook of Endocrinology, 14e.