1. **State the problem:** Simplify the expression $6 + 6 \div 3 \times 4$. 2. **Recall the order of operations:** Use PEMDAS/BODMAS rules: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). 3. **Apply division and multiplication from left to right:** $$6 + \cancel{6 \div 3} \times 4 = 6 + 2 \times 4$$ 4. **Continue multiplication:** $$6 + \cancel{2 \times 4} = 6 + 8$$ 5. **Finally, perform addition:** $$6 + 8 = 14$$ **Answer:** The simplified value of the expression is $14$.