Answer: b < -6 or b > 6
Reason
b is some unknown number on the number line
|b| represents the distance b is from 0 on the number line.
For instance, b = -7 is 7 units away from 0 because |b| = |-7| = 7
Distance is never negative. This is why absolute value is needed.
The notation |b| > 6 means "b is more than 6 units away from zero". So either b < -6 or b > 6
If b < -6 then it includes things like b = -7, b = -8, b = -9, etc. All of which make |b| > 6 true, since all of those values are more than 6 units away from zero.
Similarly, b > 6 means things like b = 7, b = 8, b = 9, etc make |b| > 6 true.
I recommend drawing out a number line to help illustrate what is going on here.
The more general rule is |x| > k breaks down to x < -k or x > k where k > 0.