Drive this from the single action of parathyroid hormone: it pushes calcium up and phosphate down. Whatever happens to PTH, calcium and phosphate move in opposite directions to each other.
The stem gives low calcium together with high phosphate. For calcium to be low you need too little PTH effect, and too little PTH also means the kidney stops dumping phosphate, so phosphate climbs. That exact pair, low calcium and high phosphate, is the signature of hypoparathyroidism. That is the answer.
The recalled key listed hyperparathyroidism, but that produces the mirror image, namely high calcium and low phosphate, so it cannot be right and the key is corrected. Thyroid gland over or under activity does not generate this calcium-phosphate pattern, so hyperthyroidism and hypothyroidism are both out.
Low calcium plus high phosphate equals failure of parathyroid hormone.
\[\boxed{\text{Hypoparathyroidism}}\]