Explanation:

- We are given the parabola \( y^2 = 4kx \).

- The latus rectum of this parabola is a line segment perpendicular to the axis of the parabola and it passes through the focus.

- The length of the latus rectum for the parabola \( y^2 = 4kx \) is equal to \( 4k \).

- The problem states that the area of the region bounded by the parabola and its latus rectum is 24 square units.

- To find the area, consider that it is bounded by \( x = k \) (since the latus rectum is vertical at the focus (k,0)) from \( y = -2k \) to \( y = 2k \).

- The integral of the function \( y = \sqrt{4kx} \) with respect to \( x \) from 0 to \( k \) calculates the area under the curve, resulting in \( \frac{8k^2}{3} \) for both sides of the y-axis.

- Equate the total area \( \frac{8k^2}{3} \) to 24 to find \( k \).

- Calculate \( k^2 = 9 \).

- Thus, \( k = 3 \) since \( k > 0 \).

Option:3- 3 is the correct answer.