Step-by-step Solution:

Quick Solution

This problem asks for the shortest distance between the start and end points. This can be found by tracking the net movement along the cardinal directions (East-West and North-South) and then using the Pythagorean theorem.

1. Trace the Path and Calculate Net Displacements

Let's break down the journey from the starting office:

1. Travels 10 km towards West.(Current position: 10 km West of start)
2. Turns left (now facing South) and walks 8 km.(Current position: 10 km West and 8 km South of start)
3. Turns left again (now facing East) and walks 4 km.(This cancels out 4 km of the westward journey)

Now, let's calculate the final net displacement from the office:

• Net East-West Displacement: 10 km West - 4 km East = 6 km West.
• Net North-South Displacement: 8 km South.

2. Apply the Pythagorean Theorem

The net movements form the two sides of a right-angled triangle. The shortest distance back to the office is the hypotenuse of this triangle.

- Side A = 6 km
- Side B = 8 km
- Shortest Distance (Hypotenuse) = √(A² + B²)

Distance = √(6² + 8²)
Distance = √(36 + 64)
Distance = √(100)
Distance = 10 km

Final Answer: The shortest distance to his office is 10 km.