Calculate the area of the first rectangle.

The measurements of the first rectangle are $3k$ by 3.
The area of a rectangle is length $\times$ width.

$$\text{Area}_1 = (3k) \times 3 = 9k$$

The measurements of the second rectangle are $k+3$ by 6.

$$\text{Area}_2 = (k+3) \times 6$$

Since the two rectangles have the exact same area:

$$\text{Area}_1 = \text{Area}_2$$ $$9k = 6(k+3)$$

Subtract $6k$ from both sides of the equation:

$$9k - 6k = 18$$ $$3k = 18$$

Divide by 3:

$$k = \frac{18}{3}$$ $$k = 6$$

The value of $k$ is: