The triangles CBA and CDE are similar, so all corresponding lengths are proportional. Each length in CBA is 1/2 as big as the corresponding length in CDE. Think about DF, the altitude in CDE, and the length to which it would correspond in CBA: an altitude from vertex B to the base AC.
Call that h. Since DF = 4, h = 2.
Now, for CBA, we have an altitude h = 2 and a base AC = 6.