The capillary rise of water in a soil depends on several factors, including the void ratio and the effective size of the soil particles.

Given:
- Void ratio of soil A is twice that of soil B
- Effective size of particles of soil A is one-third of that of soil B

To find:
- The ratio of the height of capillary rise of water in soil A to that of soil B

Let's analyze this step by step:

1. Understanding Void Ratio:
The void ratio of a soil is the ratio of the volume of voids (empty spaces) to the volume of solids in the soil. A higher void ratio indicates a higher amount of voids and, therefore, more space for water to rise through capillary action.

2. Understanding Effective Size of Particles:
The effective size of particles refers to the size of the soil particles that affects the flow of water through the soil. Smaller particles have a higher surface area, allowing for more capillary rise of water.

3. Comparing Void Ratios:
Given that the void ratio of soil A is twice that of soil B, it means that soil A has more voids than soil B. This implies that soil A has more space for water to rise through capillary action compared to soil B.

4. Comparing Effective Sizes of Particles:
The effective size of particles of soil A is one-third of that of soil B. Smaller particles have a higher surface area, which facilitates capillary rise. Therefore, soil A, with smaller particles, has a higher capillary rise compared to soil B.

5. Ratio of Capillary Rise:
Considering the above points, we can conclude that the capillary rise of water in soil A will be higher than in soil B.
The ratio of the height of capillary rise in soil A to that of soil B can be calculated as follows:

Ratio = (Void Ratio of A / Void Ratio of B) * (Effective Size of B / Effective Size of A)

Since the void ratio of A is twice that of B, and the effective size of A is one-third of that of B, the ratio simplifies to:

Ratio = (2/1) * (1/3) = 2/3 ≈ 0.67

Therefore, the correct answer is option (a) 0.67.