12√8* √3/2

To simplify the expression \( 12\sqrt{8} \cdot \frac{\sqrt{3}}{2} \), we can follow these steps:

1. Simplify \( \sqrt{8} \): \[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \]

2. Substitute back into the expression: \[ 12\sqrt{8} = 12 \cdot 2\sqrt{2} = 24\sqrt{2} \]

3. Now substitute this back into the expression: \[ 24\sqrt{2} \cdot \frac{\sqrt{3}}{2} \]

4. Multiply by \(\frac{1}{2}\): \[ = 24\sqrt{2} \cdot \frac{\sqrt{3}}{2} = \frac{24\sqrt{2} \cdot \sqrt{3}}{2} \]

5. Now simplify the fraction: \[ = 12\sqrt{6} \]

So, the final simplified result of \( 12\sqrt{8} \cdot \frac{\sqrt{3}}{2} \) is:

\[ \boxed{12\sqrt{6}} \]