Question 470469
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I don't know how <i>you</i> would solve the problem.  I can show you how
<i><b>I</b></i> solve it.  Then you can decide for yourself whether that is the method you will use.

First recall the definition of absolute value:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |x|\ =\ \left\{\ \ x\text{ if }x\ \geq\ 0\cr-x\text{ if }x\ <\ \,0\right]

That means we can say that

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |3(y\ +\ 4)|\ =\ 12]

means that

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3(y\ +\ 4)\ =\ 12]

or

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3(y\ +\ 4)\ =\ -12]

Now all that is left is to solve the two ordinary equations to get the two elements of the solution set.

John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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