To solve the problem, let's carefully translate the statement into a mathematical equation by breaking it down step-by-step:
1. Identify the unknown number:
- Let's denote the unknown number by [tex]\( x \)[/tex].
2. Translate "The product of a number and 6":
- The product of the unknown number [tex]\( x \)[/tex] and 6 is written as [tex]\( 6x \)[/tex].
3. Translate "decreased by 4":
- Decrease the product [tex]\( 6x \)[/tex] by 4, which is written as [tex]\( 6x - 4 \)[/tex].
4. Translate "is equal to 20":
- Set the expression [tex]\( 6x - 4 \)[/tex] equal to 20.
Combining these steps, the statement translates to the equation:
[tex]\[ 6x - 4 = 20 \][/tex]
Now let's match this equation with the given options:
- (a) [tex]\( 6x + 4 = 20 \)[/tex] — This is incorrect because it adds 4 instead of decreasing by 4.
- (b) [tex]\( 6x - 4 = 20 \)[/tex] — This is correct as it matches the translation exactly.
- (c) [tex]\( 6(x + 4) = 20 \)[/tex] — This is incorrect because it implies that 6 is multiplied by the sum of [tex]\( x \)[/tex] and 4.
- (d) [tex]\( 6 - 4x = 20 \)[/tex] — This is incorrect because it has the wrong operations and placement of variables.
Therefore, the correct option that matches the statement is:
\[ \boxed{b \) [tex]\( 6x - 4 = 20} \)[/tex]
