Answer
See graph.
$(-\infty,\infty)$, $[-2,10]$.
Work Step by Step
Step 1. See graph for $y=-6sin(\frac{\pi}{3} x)+4$ with key points or transform from $y=sin(x)$ (shrink horizontally by a factor of $\frac{3}{\pi}$, stretch vertically by a factor of 6, reflect across the x-axis, then shift 4 units up.)
Step 2. Based on the graph, we can determine the domain as $(-\infty,\infty)$ range as $[-2,10]$.