To find the length between the points \((0, 6)\) and \((-3, -2)\), we can use the distance formula, which is derived from the Pythagorean theorem. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
In this case, we have the points \((x_1, y_1) = (0, 6)\) and \((x_2, y_2) = (-3, -2)\).
Now, we can plug in the coordinates into the formula:
\[ d = \sqrt{((-3) - 0)^2 + ((-2) - 6)^2} \]
Calculating the differences:
\[ d = \sqrt{(-3)^2 + (-8)^2} \]
Now, squaring the differences:
\[ d = \sqrt{9 + 64} \]
Adding those values together:
\[ d = \sqrt{73} \]
Now, we can calculate the square root of 73:
\[ d \approx 8.544 \]
Finally, rounding this to the nearest hundredth, we get:
\[ d \approx 8.54 \]
Thus, the length between the points \((0, 6)\) and \((-3, -2)\) is approximately 8.54.