Given Information:
- Rectangle ABCD
- Point E on AB
- AC = 2/3
- AB = 6 km
- AD = 3 km

Objective:
To find the length of DE.

Step-by-Step Solution:

1. Understanding the Problem:
We are given a rectangle ABCD and a point E on side AB. We need to find the length of DE.

2. Analyzing the Given Information:
- AC is equal to 2/3 of AB, which means AC = (2/3) * 6 km = 4 km.
- AD is given as 3 km.

3. Understanding the Rectangle:
In a rectangle, opposite sides are equal in length. So, the length of AB is equal to the length of CD, and the length of AD is equal to the length of BC.

4. Identifying the Relevant Triangle:
To find the length of DE, we need to consider triangle ADE. Since we know the lengths of AD and AC, we can use the Pythagorean theorem to find the length of DE.

5. Applying the Pythagorean Theorem:
In triangle ADE, we have:
- AD = 3 km
- AC = 4 km

Using the Pythagorean theorem, we can express the relationship between these sides as:
AD^2 + DE^2 = AE^2

Substituting the given values, we get:
3^2 + DE^2 = AE^2

6. Solving for AE:
Since AC = 2/3 * AB, we can express AE in terms of AB:
AE = AB - BE

Substituting the given values, we get:
AE = 6 km - BE

Now, we can substitute AE in the Pythagorean theorem equation:
3^2 + DE^2 = (6 km - BE)^2

7. Solving for BE:
We know that AC = 2/3 * AB. Substituting the given values, we get:
4 km = (2/3) * 6 km + BE

Simplifying the equation, we get:
4 km = 4 km + BE

Subtracting 4 km from both sides, we get:
BE = 0 km

8. Simplifying the Pythagorean Theorem Equation:
Now that we know BE = 0 km, we can simplify the Pythagorean theorem equation:
3^2 + DE^2 = (6 km - 0 km)^2

Simplifying further, we get:
9 + DE^2 = 6^2

Simplifying, we get:
9 + DE^2 = 36

Subtracting 9 from both sides, we get:
DE^2 = 27

9. Finding the Length of DE:
To find the length of DE, we take the square root of both sides:
DE = √27

Simplifying, we get:
DE ≈ 5.20 km

Therefore, the length of DE is approximately 5.20 km.