Final answer:
The 6-year-old girl is likely in septic shock characterized by severe symptoms such as mottled skin, fever, weak pulses, and rapid heart rate, which require emergency medical treatment.
Step-by-step explanation:
The condition described for the irritable 6-year-old girl with mottled skin color, high fever, cold extremities, prolonged capillary refill time, absent distal pulses, weak central pulses, tachycardia, tachypnea, and hypotension is indicative of shock, most likely septic shock given the fever and mottled skin. The severity of her symptoms suggests this is a medical emergency requiring immediate intervention to manage the shock and the underlying cause. The combined symptoms of altered mental status, high heart rate, compromised circulation, and inadequate oxygenation demand rapid assessment and treatment in a critical care setting.