Let's solve the problem step by step:
We are asked to find the product of [tex]\( 4(3x - 2) \)[/tex].
### Step 1: Understand the Expression
The given expression is [tex]\( 4(3x - 2) \)[/tex]. This means we need to multiply each term inside the parentheses by [tex]\( 4 \)[/tex].
### Step 2: Distribute the Constant
Distribute the [tex]\( 4 \)[/tex] across the terms inside the parenthesis:
1. Multiply [tex]\( 4 \)[/tex] by [tex]\( 3x \)[/tex]:
[tex]\[
4 \cdot 3x = 12x
\][/tex]
2. Multiply [tex]\( 4 \)[/tex] by [tex]\( -2 \)[/tex]:
[tex]\[
4 \cdot (-2) = -8
\][/tex]
### Step 3: Combine the Results
After distribution, the terms inside the parentheses have been multiplied by [tex]\( 4 \)[/tex], resulting in:
[tex]\[
12x - 8
\][/tex]
This is the product of the expression [tex]\( 4(3x - 2) \)[/tex].
### Conclusion
Therefore, the correct answer is [tex]\( 12x - 8 \)[/tex]. Among the given options:
- [tex]\( 12x - 8 \)[/tex]
- [tex]\( 64x - 32 \)[/tex]
- [tex]\( -8x + 16 \)[/tex]
- [tex]\( -6x^2 + 18x \)[/tex]
The correct choice is [tex]\(\boxed{12x - 8}\)[/tex].
