Get the absolute value term by itself by adding 7 to both sides:

    |b + 4| > 18

There are four rules for removing absolute value bars in
absolute value inequalities:

If A is positive:

1.  |EXPRESSION| < A becomes 

-A < EXPRESSION < A

2.  |EXPRESSION| ≦ A becomes 

-A ≦ EXPRESSION ≦ A

3.  |EXPRESSION| > A becomes

EXPRESSION < -A  OR EXPRESSION > A 

4.  |EXPRESSION| ≧ A becomes

EXPRESSION ≦ -A  OR EXPRESSION ≧ A

-----------------------------------------

    |b + 4| > 18

is rule 3 above where EXPRESSION = b + 4 and A = 4

    |b + 4| > 18 becomes

b + 4 < -18  OR  b + 4 > 18

Solve each for b:

    b < -22 OR  b > 14  

Draw the graph on a number line:

<==============o-----------------------o===============>
             -22                      14 

Then the interval notation for this is an abbreviation 
for this graph

                   (-∞,-22) U (14,∞)

Edwin