Which equation has no solution?
|4x - 2| = - 6, |-2 - x| = 9, |3x + 6| = 6, |-2x + 8| = 0

Solution:

The absolute value of any equation can never be negative.

An absolute value of a real number is just the distance from zero to the number on the number line regardless of its direction. It returns only a positive value.

⇒ |4x - 2| = -6 has a negative value -6.

Example: Any equation with value equal to negative like

|5x - 9| = -7

|7x - 3| = -3

|3x - 6| = -5 etc will not have solutions for x.

Thus, the equation |4x - 2| = -6 has no solution.

Which equation has no solution?
|4x - 2| = - 6, |- 2 - x| = 9, |3x + 6| = 6, |- 2x + 8| = 0

Summary:

The |4x - 2| = -6 has no solution for x because |x| can not be negative.