Let's visualize this situation step by step:

The man walked 2 km east.
Then, he walked 2 km south.
Next, he walked 4 km east.
Finally, he walked 10 km north.
To find the straight-line distance from the starting point, we can treat this as a displacement problem. We can use the Pythagorean theorem because the man's path forms a right-angled triangle.

The 2 km east and 4 km east segments form the horizontal legs of the right triangle.
The 2 km south and 10 km north segments form the vertical legs of the right triangle.
Let's calculate the lengths of these legs separately:

Horizontal leg (East): 2 km + 4 km = 6 km

Vertical leg (North-South): 10 km (north) - 2 km (south) = 8 km (net northward)

Now, we can use the Pythagorean theorem to find the length of the hypotenuse (the straight-line distance):

c^2=a^2+b^2

Where:

c is the length of the hypotenuse (the straight-line distance).
a is the horizontal leg (6 km).
b is the vertical leg (8 km).
Substitute the values:

c^2=6^2+8^2

c^2=36+64

c^2=100

Now, find the square root of both sides to get c:

c=100​=10 kilometers

So, the straight-line distance from the starting point is 10 kilometers. The correct answer is indeed 10, as provided in the answer choices.