Simplify. \( \left(-\frac{1}{2} \sqrt{2}\right)(-6 \sqrt{18}) \)

To simplify \( \left(-\frac{1}{2} \sqrt{2}\right)(-6 \sqrt{18}) \), we start by multiplying the two parts together. First, notice that the negative signs cancel out: \[ \left(-\frac{1}{2}\right)(-6) = \frac{1}{2} \times 6 = 3. \] Next, simplify \( \sqrt{18} \): \[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}. \] Now, substitute back into our expression: \[ 3 \times \sqrt{2} \times 3\sqrt{2} = 3 \times 3 \times \sqrt{2} \times \sqrt{2} = 9 \times 2 = 18. \] So, the final simplified result is: \[ \boxed{18}. \]