To find the equilibrium constant for the overall reaction $$\mathrm{X} \rightleftharpoons \mathrm{W}$$, we need to combine the equilibrium constants for the individual reactions given. Let's analyze this step-by-step:

The given reactions and their equilibrium constants are:

$$\begin{aligned} & \mathrm{X} \rightleftharpoons \mathrm{Y} \quad K_1 = 1.0 \\ & \mathrm{Y} \rightleftharpoons \mathrm{Z} \quad K_2 = 2.0 \\ & \mathrm{Z} \rightleftharpoons \mathrm{W} \quad K_3 = 4.0 \end{aligned}$$

The equilibrium constant for the overall reaction $$\mathrm{X} \rightleftharpoons \mathrm{W}$$ is the product of the equilibrium constants for the individual steps. This is because the equilibrium constant for a composite reaction is the product of the equilibrium constants for the sequential reactions that lead to the composite reaction.

So, we have:

$$K_{\text{overall}} = K_1 \cdot K_2 \cdot K_3$$

Now, substituting the given values:

$$K_{\text{overall}} = 1.0 \cdot 2.0 \cdot 4.0 = 8.0$$

Therefore, the equilibrium constant for the reaction $$\mathrm{X} \rightleftharpoons \mathrm{W}$$ is 8.0, which corresponds to Option B.