Mass Moment of Inertia (MOI) is a measure of an object's resistance to rotational motion. It depends on the mass distribution of the object and the axis of rotation. In this case, we are given a rectangular plate and asked to find its MOI about the x-axis passing through the center of gravity (C.G) of the plate.

Since the y-axis is parallel to d and perpendicular to b, we can assume that the dimensions of the rectangular plate are b (width) and d (height). The plate's center of gravity is located at the midpoint of the plate, which is also the intersection point of the x and y axes.

To find the MOI of the rectangular plate about the x-axis passing through the C.G, we can use the parallel axis theorem. According to this theorem, the MOI about any axis parallel to an axis passing through the center of gravity can be found by adding the MOI about the center of gravity to the product of the mass and the distance squared between the two axes.

Let's calculate the MOI using the parallel axis theorem:

1. MOI about the center of gravity:
The MOI of a rectangular plate about an axis passing through its center of gravity and perpendicular to the plane of the plate can be calculated using the formula:

Ic.g = (m * (b^2 + d^2)) / 12

Here, m represents the mass of the plate.

2. Distance squared between the two axes:
The distance between the x-axis passing through the C.G and the center of gravity is zero since the C.G is located on the x-axis.

3. MOI about the x-axis passing through the C.G:
Using the parallel axis theorem, we can calculate the MOI about the x-axis passing through the C.G as:

Ix = Ic.g + (m * (0^2))

Simplifying the equation:
Ix = Ic.g = (m * (b^2 + d^2)) / 12

Comparing the equation with the given options, we can see that the correct answer is option B:

Mass MOI of a rectangular plate about x-axis passing through the C.G = Md^2/12