-6 < -4x - 6 < 46

The object is to solve for x in the middle:

Add 6 to all three sides:

-6 + 6 < -4x - 6 + 6 < 46 + 6

      0 < -4x < 52

Divide all three sides by -4.  We must reverse the inequality
symbols when (and only when) we divide (or multiply) through
by a negative number. -4 is negative so we must reverse
the inequality symbols from < to > :


       >  > 

          0 > x > -13

That's the solution.  That can also be written as 

          -13 < x < 0.

The solution SET can be indicated by a number line graph:

----------o===================================================o--------
-15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2

or by set-builder notation:

        { x | -13 < x < 0 }

or by interval notation:

             (-13, 0)  

Edwin