After a craniopharyngioma is removed, the pituitary and hypothalamus are often left unable to drive their target glands, so the child can lose multiple hormone axes at once. The examiner is testing priority: when several replacements are needed, which goes in first.
The answer is governed by which missing hormone can kill fastest. Loss of the adrenal axis, meaning insufficient cortisol because ACTH is gone, is the immediate danger because cortisol is essential for vascular tone and the stress response; without it the patient can slide into hypotensive adrenal crisis. So glucocorticoids take top priority.
There is also a pharmacological trap that reinforces this order. If thyroxine is started before cortisol is replaced, the rise in metabolic rate accelerates cortisol utilisation and can unmask or trigger a full adrenal crisis. Hence steroids must always precede thyroxine. Growth hormone and gonadal steroids are addressed much later once the patient is stable, and prolactin is not given as replacement therapy at all.
Therefore the first hormone to administer is the steroid.\[\boxed{\text{Steroids}}\]