To find the length of the diagonal of the rectangle formed by the points \((-6, 8)\), \((4, 8)\), \((4, -3)\), and \((-6, -3)\), we can use the coordinates of two opposite corners of the rectangle.
Let's choose the points \((-6, 8)\) and \((4, -3)\) as the opposite corners. The length of the diagonal can be calculated using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Substituting the coordinates of the chosen points into the formula:
- \(x_1 = -6\)
- \(y_1 = 8\)
- \(x_2 = 4\)
- \(y_2 = -3\)
Now substitute:
\[ d = \sqrt{(4 - (-6))^2 + (-3 - 8)^2} \] \[ d = \sqrt{(4 + 6)^2 + (-3 - 8)^2} \] \[ d = \sqrt{(10)^2 + (-11)^2} \] \[ d = \sqrt{100 + 121} \] \[ d = \sqrt{221} \]
Now, we compute \(\sqrt{221}\):
\[ \sqrt{221} \approx 14.866 \]
Rounding to the nearest hundredth, the length of the diagonal of the rectangle is:
\[ \boxed{14.87} \]