Final answer:
The expression |b| > 6 is equivalent to b > 6 or b < -6, which means 'b' can be greater than 6 or less than -6.
Step-by-step explanation:
The question asks which expression is equivalent to |b| > 6. The absolute value of a number represents its distance from zero on the number line without regard to direction. So, when we say |b| > 6, it means that the value of 'b' is more than 6 units away from zero, regardless of whether 'b' is positive or negative.
To express this inequality without absolute values, we consider both the positive and negative scenarios because |b| can be though of as both 'b' and '-b'. Therefore, if 'b' is positive and greater than 6, the inequality is simply b > 6. Conversely, if 'b' is negative and its distance from zero is greater than 6, then 'b' must be less than -6, which we write as b < -6. Combining these two conditions, the equivalent expressions are b > 6 or b < -6.