1. **State the problem:** We need to find the value of $\sin\left(\frac{4\pi}{6}\right)$.\n\n2. **Simplify the angle:** Simplify the fraction inside the sine function.\n$$\frac{4\pi}{6} = \frac{2\pi}{3}$$\n\n3. **Recall the sine value:** The sine of $\frac{2\pi}{3}$ is the sine of 120 degrees, which is known to be $\frac{\sqrt{3}}{2}$.\n\n4. **Conclude the result:** Therefore,\n$$\sin\left(\frac{4\pi}{6}\right) = \sin\left(\frac{2\pi}{3}\right) = \frac{\sqrt{3}}{2}$$