2x+4 < 12 and -3(x+4) < 32
  -4   -4      -3x-12 < 32
---------         +12  +12
2x   <  8      -----------  
 x   <  4      -3x    < 42
                 x    > -14   <---reversing inequality since
                                  we divided both sides by a
                                  negative number, -3

So we wind up with x < 4 and x > -4

We turn the second inequality around as -4 < x and we have:

        -4 < x  and x < 4

Which we can write with x in the middle as

           -4 < x < 4

On the number line, we have

----------o=======================o---------
-7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7

Edwin