1. **State the problem:** Order the set of numbers from least to greatest: $-3, 6, 3, \frac{1}{2}, 3, 2, -3, \frac{3}{4}, -\frac{3}{2}$. 2. **List the numbers clearly:** - $-3$ - $6$ - $3$ - $\frac{1}{2}$ - $3$ - $2$ - $-3$ - $\frac{3}{4}$ - $-\frac{3}{2}$ 3. **Convert fractions to decimals for easier comparison:** - $\frac{1}{2} = 0.5$ - $\frac{3}{4} = 0.75$ - $-\frac{3}{2} = -1.5$ 4. **Arrange all numbers in decimal form:** - $-3$ - $-3$ - $-1.5$ - $0.5$ - $0.75$ - $2$ - $3$ - $3$ - $6$ 5. **Order from least to greatest:** $$-3, -3, -1.5, 0.5, 0.75, 2, 3, 3, 6$$ 6. **Final answer:** $$\boxed{-3, -3, -\frac{3}{2}, \frac{1}{2}, \frac{3}{4}, 2, 3, 3, 6}$$