1. **State the problem:** Simplify the expression $24 \div 6 + 4 \times (3 + 6)$.\n\n2. **Recall order of operations (PEMDAS/BODMAS):** Parentheses first, then multiplication and division from left to right, then addition and subtraction.\n\n3. **Evaluate inside the parentheses:**\n$$3 + 6 = 9$$\n\n4. **Rewrite the expression with the evaluated parentheses:**\n$$24 \div 6 + 4 \times 9$$\n\n5. **Perform division and multiplication from left to right:**\nFirst, division:\n$$24 \div 6 = 4$$\nThen multiplication:\n$$4 \times 9 = 36$$\n\n6. **Rewrite the expression:**\n$$4 + 36$$\n\n7. **Perform the addition:**\n$$4 + 36 = 40$$\n\n**Final answer:** $40$