Step-by-step solution-:

By using the **Geometric Mean (Altitude) Theorem**:

(CD)^2=AD\times{DB}

Substitute the **CD=12, AD=x**, and **DB=16 **into the **Geometric Mean (Altitude) Theorem**:

\textcolor{primary}{12^{2}}=\textcolor{secondary}{x}\cdot \textcolor{tertiary}{16}\implies144=16x

After solving:

16x=144\implies x=\frac{\cancel{144}}{\cancel{16}}=9

The value of **x** is 9:

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