To find the area bounded by the parabola y^2 = 8x and its latus rectum, we can follow these steps:

Step 1: Understanding the Parabola and Latus Rectum
- A parabola is a U-shaped curve defined by a quadratic equation in the form y^2 = 4ax, where "a" is the distance between the focus and the vertex.
- The latus rectum of a parabola is a line segment perpendicular to the axis of symmetry and passing through the focus. It is twice the focal length.

Step 2: Finding the Focus and Focal Length
- Comparing the given equation y^2 = 8x with the standard form y^2 = 4ax, we can determine that a = 2.
- Since the equation y^2 = 4ax represents a parabola opening towards the positive x-axis, the focus lies on the positive x-axis.
- The distance between the focus and the vertex is given by a, so the focus is located at (2a, 0) = (4, 0).
- The focal length is half the distance between the focus and the vertex, which is a = 2.

Step 3: Finding the Endpoints of the Latus Rectum
- Since the latus rectum is a line segment passing through the focus and perpendicular to the axis of symmetry, its endpoints have coordinates (4 ± a, 2a) = (4 ± 2, 4) = (2, 4) and (6, 4).

Step 4: Determining the Area Bounded by the Parabola and Latus Rectum
- The area bounded by the parabola and the latus rectum can be found by subtracting the area under the parabola between the x-coordinates of the endpoints of the latus rectum from the area of the latus rectum itself.
- The area of the latus rectum is given by the formula 2 × (focal length) × (latus rectum length) = 2 × 2 × 4 = 16 square units.
- To find the area under the parabola, we integrate the equation y^2 = 8x with respect to x, in the range [2, 6].
- Integrating y^2 = 8x with respect to x gives us the equation x^2 = 4x^3/3.
- Evaluating the integral from x = 2 to x = 6 gives us the area under the parabola as 32/3 square units.
- Therefore, the area bounded by the parabola and its latus rectum is 16 - 32/3 = 32/3 square units.

Hence, the correct answer is option 'B': 32/3 square units.