Answer:
[tex]x=4[/tex]
Step-by-step explanation:
To solve this problem, one must use the angle bisector theorem. This theorem provides a proportion between the sides formed by an angle bisector. One can apply this theorem here by forming the following proportion,
[tex]\frac{BA}{BC}=\frac{AD}{DC}[/tex]
Substitute,
[tex]\frac{x}{6}=\frac{2}{3}[/tex]
Cross products,
[tex]3(x)=2(6)[/tex]
Simplify,
[tex]3x=12[/tex]
Inverse operations,
[tex]3x=12\\\\x = 4[/tex]
