The problem needs additional information, namely that points A,B,C are collinear. Then the concept "line segment addition" can be used to achieve what you ask to be proved.
If the three points are located on a line in the following manner A........B....C
then AB + BC = AC
and AB=8 & AC=12 (givens)
therefore 8 + BC = 12 (substitutions)
and finally, BC = 12-8 which is 4, by algebra (subtraction property)