Explanation:

- Julie starts at point Z and heads 10 km East to point Y.

- From Y, she turns left, heading 3 km North to point R.

- At R, she turns left again, heading 12 km West to point S.

- At S, she turns left once more, traveling 3 km South to reach point E.

- Finally, she turns right and travels 4 km East to point J.

- Point K is 8 km South of Z, directly aligned vertically with Y, and is southwest of Y.

- To find the shortest distance between K and Y: form a right triangle where the vertical side is 8 km and the horizontal side is 10 km (Z to Y).

- Use the Pythagorean theorem: $\sqrt{({10}^2+8^2)}=\sqrt{100+64}=\sqrt{164}\approx 12.8$.

- Correct Answer: ? 11 Km (closest approximation)