D is on side AB of ABC We know ABC similar to ACD and we know all the marked side lengths
Because AC = 6 and AD = 3, the ratio of AC to AD is 2:1. Similarly, because AB = BD + AD, the ratio of AB to AD is BD + 1 to 1.
Because 6/3 = 2/1 = BD + 1/1, we can conclude that AB = 6 and BD = 3. Therefore,BD=3.