To solve the problem in the image:

1. Understanding the Problem: The image shows two rectangles: an "Original Rectangle" with dimensions 8 units by 6 units and a "Scaled Copy" with dimensions 3 units by an unknown length (the corresponding dimension).

2. Corresponding Side Information: The side of 6 units in the original rectangle corresponds to 3 units in the scaled copy. This gives us the scale factor.

3. Finding the Scale Factor: The scale factor is the ratio of the corresponding sides. We know the original side is 6 units, and its scaled version is 3 units. Thus:

   $\text{Scale Factor} = \frac{\text{Length of Scaled Side}}{\text{Length of Original Side}} = \frac{3}{6} = \frac{1}{2}$

4. Applying the Scale Factor: Now we can apply the scale factor to find the other side of the scaled rectangle. The corresponding side in the original rectangle is 8 units, so we multiply this by the scale factor to find the side in the scaled copy:

   $\text{Scaled Side} = 8 \times \frac{1}{2} = 4 \text{ units}$

Thus, the dimensions of the scaled copy are 4 units by 3 units, and the scale factor is $\frac{1}{2}$.

Would you like more details or have any questions? Here are some related questions to explore:

1. How would the area of the scaled copy compare to the original rectangle?
2. What happens to the perimeter when a rectangle is scaled by a factor of $\frac{1}{2}$?
3. If the scale factor were $\frac{1}{3}$, what would the dimensions of the scaled copy be?
4. How do you find the scale factor if the original and scaled rectangles' side lengths are unknown?
5. Can the scale factor ever be greater than 1, and what would that mean?

Tip: Always use corresponding side lengths to calculate scale factors when working with scaled figures!