To order the numbers \(-32\), \(0.5\), \(9 - \sqrt{9}\), and \(-2\) on a number line, we need to evaluate where each number falls.
- Evaluate \(9 - \sqrt{9}\):
- \(\sqrt{9} = 3\), so \(9 - \sqrt{9} = 9 - 3 = 6\).
Now we have the numbers:
- \(-32\)
- \(-2\)
- \(0.5\)
- \(6\)
- Order the numbers from least to greatest:
- The least number is \(-32\).
- Next is \(-2\).
- Then comes \(0.5\).
- Finally, \(6\).
Thus, the correct order of the numbers on the number line is:
\[ -32, -2, 0.5, 6 \]