1. The problem is to solve the equation $$6 \arcsin x = \pi$$ for $x$. 2. Recall that $\arcsin x$ is the inverse sine function, which returns an angle $\theta$ such that $\sin \theta = x$ and $\theta \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$. 3. Divide both sides of the equation by 6 to isolate $\arcsin x$: $$\cancel{6} \arcsin x = \frac{\pi}{\cancel{6}} \implies \arcsin x = \frac{\pi}{6}$$ 4. Now, solve for $x$ by taking the sine of both sides: $$x = \sin \left(\frac{\pi}{6}\right)$$ 5. Using the known value $\sin \frac{\pi}{6} = \frac{1}{2}$, we get: $$x = \frac{1}{2}$$ 6. Since $\arcsin x$ is defined only for $x \in [-1,1]$, and $\frac{1}{2}$ is within this domain, this is the valid solution. Final answer: $$x = \frac{1}{2}$$