Final answer:
The correct instruction for cast care at home is to avoid getting the cast wet to maintain its integrity and promote proper healing.
Step-by-step explanation:
When caring for a cast at home, it is important for the mother to understand the best practices to ensure proper healing of her child's fractured left lower arm. The correct guidance from the nurse would be to avoid getting the cast wet, as this can weaken the cast and lead to skin irritation or infection. Keeping the cast dry and clean is crucial for the healing process. Other instructions that are generally provided include not inserting any objects into the cast, checking for signs of decreased circulation or increased pain, and keeping the arm elevated to reduce swelling.