We don't know the relationship between A, B and C, so we first assume a triangle then a line.

TRIANGLE

The sides of the triangle must be positive, so AB=2x-6>0, AB>2(x-3) and x>3.

Therefore AC=6(x+3)>36, AC-AB=4x+24=4(x+6), so AC>AB and AC>12 so AC is the longest side.

AC must be less than AB+BC=2x+6, because the longest side cannot be longer than the sum of the other two sides, and 6x+18 is bigger than 2x+6 (x>3) by 4x+12. Therefore ABC cannot be a triangle.

LINE (number line)

If A, B and C are on the same line, AB+BC=AC; 2x+6=6x+18, 4x=-12 and **x=-3**. AB=-12, AC=0:

B-----<----A

B------>---C, back 12 forward 12 brings us back to where we started so points A and C coincide.