To calculate the average shear stress in a rectangular channel, we need to use the specific energy equation. The specific energy equation relates the flow depth, flow velocity, and gravitational acceleration to the specific energy of the flow.

The specific energy equation is given by:

E = H + (V^2)/(2g)

Where:
E = specific energy
H = flow depth
V = flow velocity
g = gravitational acceleration

In this case, we are given the specific energy (E = 0.56m) and the flow depth (H = 0.5m). We need to solve for the flow velocity (V) using the specific energy equation.

Let's rearrange the equation to solve for V:

V^2 = 2g(E - H)
V = sqrt(2g(E - H))

Now we can substitute the given values into the equation and calculate the flow velocity:

V = sqrt(2 * 9.81 * (0.56 - 0.5))
V = sqrt(2 * 9.81 * 0.06)
V = sqrt(1.176)

V ≈ 1.083 m/s

Now that we have the flow velocity, we can calculate the average shear stress using the formula:

τ = γ * R * S

Where:
τ = average shear stress
γ = specific weight of water
R = hydraulic radius
S = slope of the energy grade line

The specific weight of water (γ) is equal to the density of water (1000 kg/m^3) multiplied by the gravitational acceleration (9.81 m/s^2):

γ = 1000 * 9.81
γ ≈ 9810 N/m^3

The hydraulic radius (R) of a rectangular channel is given by:

R = (width * depth) / (2 * (width + depth))

R = (0.8 * 0.5) / (2 * (0.8 + 0.5))
R = 0.4 / (2 * 1.3)
R ≈ 0.1538 m

The slope of the energy grade line (S) is equal to the change in specific energy (ΔE) divided by the channel length (L):

S = ΔE / L

Since we are not given the change in specific energy or the channel length, we cannot calculate the slope of the energy grade line. However, in this case, we can assume a negligible change in specific energy and a flat channel, so the slope can be considered zero.

Now we can substitute the values into the equation for average shear stress:

τ = 9810 * 0.1538 * 0
τ = 0 N/m^2

Therefore, the average shear stress in this case is 0 N/m^2.

Based on the given options, it seems there might be an error in the question or the answer choices. The correct answer cannot be option 'C' (4.32 N/m^2) since the average shear stress is zero.