To find the area bounded by the curves y^2 = 4x and x^2 = 4y, we need to determine the points of intersection and integrate the difference in the y-values over the interval.

Finding the Points of Intersection:

1. Equate the two equations to find the points of intersection:
y^2 = 4x ...(1)
x^2 = 4y ...(2)

2. Solve equation (1) for x:
x = (1/4) * y^2

3. Substitute the value of x in equation (2):
(1/4) * y^4 = 4y

4. Simplify the equation:
y^4 - 16y = 0

5. Factor out y:
y(y^3 - 16) = 0

From this equation, we have two cases:
Case 1: y = 0
Case 2: y^3 - 16 = 0

6. Solve Case 2 for y:
y^3 = 16
y = 2

Therefore, the points of intersection are (0,0) and (4,2).

Setting Up the Integral:

1. Determine the limits of integration:
Since y ranges from 0 to 2, the limits of integration are 0 and 2.

2. Determine the area element:
The area element will be the difference in the y-values multiplied by the differential of x:
dA = (y^2 - x^2) dx

3. Solve equation (1) for x:
x = (1/4) y^2

4. Substitute the values into the area element:
dA = (y^2 - [(1/4) y^2]) dx
= (3/4) y^2 dx

Evaluating the Integral:

1. Integrate the area element from x = 0 to x = (1/4) * y^2:
A = ∫[0 to 2] (3/4) y^2 dx

2. Integrate with respect to x:
A = (3/4) ∫[0 to 2] y^2 dx
= (3/4) * x * y^2 |[0 to 2]
= (3/4) * (1/4) y^4 |[0 to 2]
= (3/16) [16 - 0]
= 3

Therefore, the area bounded by the curves y^2 = 4x and x^2 = 4y is 3 square units.

Hence, the correct answer is option 'B' (16/3).