One thing I can tell here is andle BCA = 2x. Now this (interior angle) will be equal to the sum of the two exterior angles that is angle ABC + angle ADC. Probably this is how OG is telling angle ABD is x.

okay i struggled enuf on this to solve, finally it all boils down to this one theorem:

An exterior angle of a triangle is equal in measure to the sum of the two non-adjacent interior angles of the triangle


1. since <BDC=<BCD ==> BD=BC
2. now apply the above theorem to triangle BAD ==> <BDC = <BAC + <ABD

2x=x+y ==> x=y

3. Since, x=y implies that "side AD= side DB= side BC"

4. it is given in option A that AD=6 ==> side BC=6

5. Hence answer is A