To determine which of the given options is equivalent to the expression [tex]\(2(3x - 4)\)[/tex], we can simplify the expression step-by-step.
1. Start with the given expression:
[tex]\[
2(3x - 4)
\][/tex]
2. Distribute the [tex]\(2\)[/tex] to both terms inside the parentheses:
[tex]\[
2 \cdot 3x + 2 \cdot (-4)
\][/tex]
3. Perform the multiplication:
[tex]\[
6x - 8
\][/tex]
Thus, the simplified form of the expression [tex]\(2(3x - 4)\)[/tex] is [tex]\(6x - 8\)[/tex].
Now, let's compare this with the provided options to see which one matches:
- [tex]\(5x - 8\)[/tex]: This is not equivalent to [tex]\(6x - 8\)[/tex].
- [tex]\(5x - 4\)[/tex]: This is not equivalent to [tex]\(6x - 8\)[/tex].
- [tex]\(6x - 8\)[/tex]: This matches our simplified expression.
- [tex]\(6x - 4\)[/tex]: This is not equivalent to [tex]\(6x - 8\)[/tex].
Therefore, the correct option is:
[tex]\[
6x - 8
\][/tex]
This option corresponds to the third listed option. Thus, the answer is [tex]\( \boxed{3} \)[/tex].
