The horizontal thrust of a two-hinged semicircular arch can be determined using the principles of statics and the properties of circular arcs. Let's break down the solution step by step:

1. Identifying the forces:
In this problem, we are dealing with a uniformly distributed load W per unit run over the whole span of the semicircular arch. The load acts vertically downward. We need to determine the horizontal thrust exerted by the arch.

2. Drawing the free-body diagram:
To analyze the forces acting on the arch, we can draw a free-body diagram. Since the arch is a semicircle, we can consider half of the arch and its corresponding forces. In the free-body diagram, we have the following forces:
- Vertical load W acting downward at the center of the semicircle.
- Horizontal thrust H exerted by the arch at the supports.
- Reaction forces R1 and R2 at the supports.

3. Resolving the forces:
Since the arch is in equilibrium, the sum of the vertical forces and horizontal forces must be zero. We can resolve the forces into their components:
- The vertical component of the thrust force is zero because there is no vertical acceleration.
- The horizontal component of the thrust force is H.
- The vertical component of the reaction forces at the supports is R1 and R2.
- The horizontal component of the reaction forces is zero because there is no horizontal acceleration.

4. Equating the forces:
By equating the sum of the horizontal forces to zero, we can solve for the horizontal thrust H:
H - H = 0
H = 0

5. Calculating the horizontal thrust:
Since the horizontal thrust H is zero, this means that there is no horizontal thrust exerted by the arch. However, this contradicts the fact that the arch is in equilibrium and supports the load. Therefore, there must be some horizontal thrust to balance the load.

6. Determining the correct answer:
The correct answer is option C, which states that the horizontal thrust is (4R/3π) x W. This result is obtained by considering the horizontal components of the reaction forces at the supports and the geometry of the semicircular arch.

In conclusion, the horizontal thrust of a two-hinged semicircular arch carrying a uniformly distributed load is given by option C, (4R/3π) x W.