Final answer:
The nurse should use The Modified Checklist for Autism in Toddlers (M-CHAT) to screen a 24-month-old toddler for autism spectrum disorder due to sensory sensitivity, social difficulties, and delayed speech.
Step-by-step explanation:
The nurse should administer The Modified Checklist for Autism in Toddlers (M-CHAT), which is specifically designed to screen for autism spectrum disorder (ASD) in young children. Given the toddler's sensory sensitivity, difficulty with social interactions, and delayed speech development, these signs align with characteristics of ASD. Early and accurate screening is crucial for identifying children who may benefit from early interventions and therapies designed to address the challenges associated with ASD.