Evaluation of an infant reveals hypocalcemia due to a lack of parathyroid hormone. On x-ray, the thymic shadow is absent. Which of the following embryonic structures is involved

Since thymus is missing, appropriate answer would be third pharyngeal pouch. This patient has got DiGeorge syndrome. DiGeorge syndrome causes migration defects of neural crest-derived tissues, paicularly affecting development of the third and fouh Branchial pouch (pharyngeal pouches)