If you mean what is AD, which is what the problem is asking for then you can use what most books define as the angle bisector theorem which says the following: An angle bisector in a triangle divides the opposite side into two segments which are in the same proportion as the other two sides of the triangle.
In this case: I think your proportion would look like this: [tex] \frac{10}{8} = \frac{CD}{DA} [/tex]. Now we need to find a way to express the two segments CD and DA... We see that AC is equal to 6, and if we let CD = x then DA will have to be 6 - x giving us the result below:
[tex] \frac{10}{8} = \frac{x}{6-x} [/tex] We cross multiply to get:
10(6 - x) = 8x and solving this equation we find x = [tex]3 \frac{1}{3} [/tex] and AD would be equal to 6 - [tex]3 \frac{1}{3} [/tex] = [tex]2 \frac{2}{3} [/tex]
