Answer
12
Work Step by Step
This is a 30-60-90 triangle. We see that x, the length of AC, must be equal to $6\sqrt3$ since it is a 30-60-90 triangle. Thus, BC has a length of:
$$ =6\sqrt3\sqrt3 \\ = 6\cdot 3 \\ =18$$
Since AD bisects a 60 degree angle, the small right triangle is also a 30-60-90 triangle. We know that AC is still $6\sqrt 3$, so the length of DC is 6. Thus, the length of BD is:
$$ =18-6 \\ =12$$
