**Explanation:**

To determine the most economic section of a rectangular channel, we need to find the hydraulic radius that minimizes the wetted perimeter. The wetted perimeter is the length of the channel bottom and sides that are in contact with the flowing water.

The hydraulic radius (R) is defined as the cross-sectional area (A) divided by the wetted perimeter (P). Mathematically, R = A/P.

To minimize the wetted perimeter, we need to maximize the hydraulic radius. Let's consider the different options given:

a) Twice the Depth: If the hydraulic radius is twice the depth, it means that A/P = 2h/2h = 1. This implies that the cross-sectional area is equal to the wetted perimeter, which is not the most economical section.

b) Half the Breadth: If the hydraulic radius is half the breadth, it means that A/P = bh/(2b + h). This expression can be simplified to A/P = h/(2 + h/b). As the hydraulic radius increases, the value of h/b decreases. Therefore, the hydraulic radius being half the breadth results in a smaller hydraulic radius compared to the other options.

c) Half the Depth: If the hydraulic radius is half the depth, it means that A/P = h/(2h + b). This expression can be simplified to A/P = h/(2 + b/h). As the hydraulic radius increases, the value of b/h decreases. Therefore, the hydraulic radius being half the depth results in a smaller hydraulic radius compared to the other options.

d) Twice the Breadth: If the hydraulic radius is twice the breadth, it means that A/P = 2b/(2b + h). This expression can be simplified to A/P = b/(1 + h/b). As the hydraulic radius increases, the value of h/b increases. Therefore, the hydraulic radius being twice the breadth results in a larger hydraulic radius compared to the other options.

Based on the above analysis, we can conclude that the most economic section of a rectangular channel is one where the hydraulic radius is half the depth (option c). This choice results in a smaller hydraulic radius compared to the other options, leading to a minimized wetted perimeter, which is the desired outcome for an economical design.