Step 1 :The question is asking for the daily dosage of Augmentin for a 30-pound child. The order is for 480 mg every 8 hours.
Step 2 :Since there are 24 hours in a day, the child will receive 3 doses in a day.
Step 3 :Therefore, the daily dosage is \(480 \mathrm{mg} \times 3 = 1440 \mathrm{mg}\).
Step 4 :Final Answer: The daily dosage of Augmentin for a 30-pound child is \(\boxed{1440} \mathrm{mg}\).