To simplify the expression [tex]\( 6(2(y + x)) \)[/tex], follow these steps:
1. Start with the original expression:
[tex]\[
6(2(y + x))
\][/tex]
2. Use the distributive property to distribute the 6 across the parenthesis:
[tex]\[
6 \times 2(y + x)
\][/tex]
3. Simplify inside the parenthesis first:
[tex]\[
2(y + x) = 2y + 2x
\][/tex]
4. Now distribute the 6 across [tex]\(2y + 2x\)[/tex]:
[tex]\[
6 \times (2y + 2x)
\][/tex]
5. Apply the distributive property again to multiply 6 by each term inside the parenthesis:
[tex]\[
6 \times 2y + 6 \times 2x
\][/tex]
6. Perform the multiplication independently:
[tex]\[
12y + 12x
\][/tex]
Thus, the simplified expression is:
[tex]\[
12y + 12x
\][/tex]
Comparing this result with the given choices:
- [tex]\(6y + 12x\)[/tex]
- [tex]\(12y + 12x\)[/tex]
- [tex]\(12y + 8x\)[/tex]
- [tex]\(8y + 8x\)[/tex]
The correct simplified expression is:
[tex]\[
12y + 12x
\][/tex]
Therefore, the correct choice is:
[tex]\[
\boxed{2}
\][/tex]
