To find the distance between the points \((0, 6)\) and \((-3, -2)\) using the Pythagorean Theorem, we can apply the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, let \((x_1, y_1) = (0, 6)\) and \((x_2, y_2) = (-3, -2)\).
Now substitute the coordinates into the formula:
\[ d = \sqrt{((-3) - (0))^2 + ((-2) - (6))^2} \]
This simplifies to:
\[ d = \sqrt{(-3)^2 + (-8)^2} \]
Calculating the squares:
\[ d = \sqrt{9 + 64} \]
Adding these together:
\[ d = \sqrt{73} \]
Now, to get the approximate distance, we can use a calculator:
\[ d \approx 8.54 \]
Therefore, the length between the points (0, 6) and (-3, -2) is approximately 8.54.
So the correct response is:
8.54