Isolate the absolute value, confirm the absolute value is not equal to a negative number, split the absolute value into 2 equations (one positive and one negative), then solve both equations.
-4|2w + 6| = -32
|2w + 6| = 8 divided both sides by -4 (confirmed that 8 is positive)
positive: negative:
2w + 6 = 8 -(2w + 6) = 8
2w = 2 (subtracted 6 from both sides) 2w + 6 = -8 (divided both sides by -1)
w = 1 (divided both sides by 2) 2w = -14 (subtracted 6 from both sides)
w = -7 (divided both sides by 2)
Answer: 1, -7