I've modified your drawing a little bit so you can see how I did this problem:
(< this sign means angle):
<(CDB) = 2x° ==> <(ABD) = x°
Therefore triangle BAD is an isoscele triangle with the base AB. Thus AD = DB.
Triangle DCB is an isoscele triangle with the base DC. Thus DB = BC.
That means: 6 = AD = DB = BC