Question: Evaluate $6 + 3\times(8 - 4)^2 \div 2$ .
1. **State the problem:** Evaluate the expression $$6 + 3\times(8 - 4)^2 \div 2$$.
2. **Apply the order of operations (PEMDAS/BODMAS):**
- Parentheses first: Calculate $(8 - 4)$.
- Exponents next: Square the result.
- Multiplication and division from left to right.
- Addition last.
3. **Calculate inside the parentheses:**
$$8 - 4 = 4$$
4. **Apply the exponent:**
$$4^2 = 16$$
5. **Rewrite the expression:**
$$6 + 3 \times 16 \div 2$$
6. **Perform multiplication and division from left to right:**
$$3 \times 16 = 48$$
7. **Continue with division:**
$$48 \div 2 = 24$$
8. **Rewrite the expression:**
$$6 + 24$$
9. **Perform the addition:**
$$6 + 24 = 30$$
**Final answer:** $$30$$