The couple starts their journey from a common point, which we can assume as the origin of our coordinate system for clarity.

1. Husband drives 3 km South from their home, which we denote as moving 3 units down the y-axis from the origin. His position becomes \((0, -3)\).
2. Then, he turns 2 km to his right, which is towards the West, moving 2 units on the negative x-axis from his current position. Thus, his final position is \((-2, -3)\).

Now, look at the wife's journey:

1. Wife moves 2 km towards the East from their home, which is 2 units on the positive x-axis. Therefore, her position becomes \((2, 0)\).

To find the distance and direction of the wife's office relative to the husband's office:

1. The relative position can be found by subtracting the husband's final coordinates from the wife's coordinates. This gives: \[ \text{Relative position} = (2 - (-2), 0 - (-3)) = (4, 3) \]
2. The distance is calculated using the distance formula: \[ \text{Distance} = \sqrt{(4)^2 + (3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ km} \]
3. The direction can be inferred as North-East, considering the relative positive x-axis direction (East) and positive y-axis direction (North).

Thus, the wife's office is located 5 km to the North-east of the husband's office.