It is easy.


On the left side, you have  three addends with identical part |x+4|.

So, you combine like terms in the left side. Then your equation takes the form

    7*|x+4| + 5 = 19.


Now move constant term 5 from left side to the right (by subtracting 5 from both sides).

You get then

    7*|x+4| = 19 - 5,

or

    7*|x+4| = 14.


Next, you divide both sides by 7.  It gives you

    |x+4| = 14/7 = 2.


Thus, the absolute value of (x+4) is 2.  It means that x+4 is EITHER 2 OR -2.

Therefore, we consider two cases.


    Case 1.  x+4 = 2.  Subtract 4 from both sides.  You will get

             x = 2 - 4 = -2.  So, x = -2 is the solution.


    Case 2.  x+4 = -2.  Again, subtract 4 from both sides.  You will get

             x = -2 - 4 = -6.  So, x = -6 is another solution.


Thus, the given equation has two solutions:  x= -2  and x= -6.


CHECK.  First, check that that x= -2 is the solution.

        You have  |-2+4| = |2| = 2.  ! correct !


        Next, check that x= -6 is the solution.  

        You have  |-6+4| = |-2| = 2.  ! correct !

Or you can do it this way

There are two cases:

Case 1:
What's between the absolute value bars is not negative:

If what's between the absolute value bars is not negative, you
can just replace the bars with parentheses:

|x+4| + 2|x+4| + 4|x+4| + 5 = 19

(x+4) + 2(x+4) + 4(x+4) + 5 = 19

     x+4 + 2x+8 + 4x+16 + 5 = 19

                    7x + 33 = 19

                         7x = -14

                          x = -2

Case 2:
What's between the absolute value bars is negative:

If what's between the absolute value bars is negative, you
change all the signs between the bars and replace the bars 
with parentheses:

   |x+4| + 2|x+4| + 4|x+4| + 5 = 19

(-x-4) + 2(-x-4) + 4(-x-4) + 5 = 19

 -x - 4 - 2x - 8 - 4x - 16 + 5 = 19

                      -7x - 23 = 19

                           -7x = 42

                             x = -6

Answers: x = -2 or x = -6

Edwin