Student or Learner
Stretch out your hand.
Asking a baby to show his hand to me, can we say stretch out your hand?
A toddler might. A 'baby' won't respond to speech in this way. What age do you consider this baby to be?
Anyway, "Show me your hand" is far preferable, and it is what you want. "Stretching out one's hand" is what one does before getting the cane - a corporal punishment usually frowned upon these days.