The correct answer is $\boxed{\frac{{\text{b}}}{6}}$.
The maximum eccentricity of load for a rectangular foundation of width $b$ is $\frac{{\text{b}}}{6}$. This is because the maximum bending moment occurs at the center of the foundation, and the bending moment is proportional to the square of the eccentricity. Therefore, the maximum eccentricity should be as small as possible to minimize the bending moment.
Option A is incorrect because it is too large. The maximum eccentricity should be less than $\frac{{\text{b}}}{2}$ to ensure that the foundation is not overstressed.
Option B is incorrect because it is too small. The maximum eccentricity should be greater than $\frac{{\text{b}}}{3}$ to ensure that the foundation is not understressed.
Option C is incorrect because it is not a valid option.
I hope this explanation is helpful. Please let me know if you have any other questions.