If an angle bisects another, that means that it splits it into 2 equal parts. Since BD bisects ABC, that means that , as shown, ABD=ACD (since it is split into 2 equal parts) and ACD+ABD=ABC . Since ABD is half of ABC,
24=(4x-12)/2=2x-6 (using the distributive property). Adding 6 to both sides, we get 30=2x and by dividing both sides by 2 we get 15=x