To solve for the length of \( AD \) in the right triangle ABC with altitude \( CD \), we can use the information provided and the Pythagorean theorem alongside properties of similar triangles.
Given:
- \( DB = 8 \)
- \( CD = 6 \)
Let:
- \( AD = x \)
- The total length of the base \( AB = AD + DB = x + 8 \)
Since triangle \( ABC \) is a right triangle, we can use the relationship between the lengths and the altitude to the hypotenuse, which states:
\[ CD^2 = AD \cdot DB \]
Now substitute the known values into the formula:
\[ 6^2 = x \cdot 8 \]
Calculating \( 6^2 \):
\[ 36 = 8x \]
Next, solve for \( x \):
\[ x = \frac{36}{8} = 4.5 \]
Thus, the length of \( AD \) is:
\[ \boxed{4.5} \]