1. **Problem Statement:** Find the exact value of $\sin\left(-\frac{2\pi}{6}\right)$. 2. **Recall the sine function property:** $\sin(-x) = -\sin(x)$. This means the sine of a negative angle is the negative of the sine of the positive angle. 3. **Simplify the angle:** $-\frac{2\pi}{6} = -\frac{\pi}{3}$. So we need to find $\sin\left(-\frac{\pi}{3}\right)$. 4. **Apply the sine property:** $$\sin\left(-\frac{\pi}{3}\right) = -\sin\left(\frac{\pi}{3}\right)$$ 5. **Recall the exact value:** $\sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$. 6. **Calculate the final value:** $$\sin\left(-\frac{\pi}{3}\right) = -\frac{\sqrt{3}}{2}$$ **Answer:** The exact value of $\sin\left(-\frac{2\pi}{6}\right)$ is $-\frac{\sqrt{3}}{2}$. This corresponds to option B.