To evaluate the expression \( 6 \cdot (4 + 2)^2 - 3^2 \), we will solve it step by step, respecting the order of operations (parentheses, exponents, multiplication and division, and addition and subtraction — PEMDAS).
1. Evaluate the expression inside the parentheses first:
[tex]\[
4 + 2 = 6
\][/tex]
2. Next, handle the exponentiation within the expression:
[tex]\[
(4 + 2)^2 = 6^2 = 36
\][/tex]
3. Now, multiply 6 by the result of the square:
[tex]\[
6 \cdot 36 = 216
\][/tex]
4. Evaluate the other exponentiation:
[tex]\[
3^2 = 9
\][/tex]
5. Finally, subtract the result of \( 3^2 \) from the result of \( 6 \cdot 36 \):
[tex]\[
216 - 9 = 207
\][/tex]
The final result is \( 207 \).
Thus, the correct answer is [tex]\( \boxed{207} \)[/tex].
