1. The problem asks us to plot the numbers $-2 \frac{1}{6}$ and $1 \frac{2}{3}$ on a number line ranging from $-3$ to $3$. 2. First, convert the mixed numbers to improper fractions or decimals for easier plotting. 3. Convert $-2 \frac{1}{6}$: $$-2 \frac{1}{6} = -\left(2 + \frac{1}{6}\right) = -\frac{12}{6} - \frac{1}{6} = -\frac{13}{6} \approx -2.1667$$ 4. Convert $1 \frac{2}{3}$: $$1 \frac{2}{3} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \approx 1.6667$$ 5. On the number line from $-3$ to $3$, locate $-2.1667$ slightly to the left of $-2$ (between $-2$ and $-3$, closer to $-2$). 6. Locate $1.6667$ slightly to the right of $1$ (between $1$ and $2$, closer to $2$). 7. These positions correspond to the fractions $-\frac{13}{6}$ and $\frac{5}{3}$ respectively, which are the exact values to plot. Final answer: The points $-2 \frac{1}{6}$ and $1 \frac{2}{3}$ are plotted at $-\frac{13}{6}$ and $\frac{5}{3}$ on the number line.