1. **State the problem:** Calculate the value of $4 \times (7 + 3^2)$.\n\n2. **Recall the order of operations:** We must first evaluate the exponent, then the addition inside the parentheses, and finally multiply.\n\n3. **Evaluate the exponent:** $3^2 = 9$.\n\n4. **Substitute back:** $4 \times (7 + 9)$.\n\n5. **Add inside the parentheses:** $7 + 9 = 16$.\n\n6. **Multiply:** $4 \times 16 = 64$.\n\n**Final answer:** $64$.