Hello,

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