Patricia has a rectangular painting that she wishes to frame. The frame must also be rectangular and will extend $3\text{ cm}$ outward from each of the four sides of the painting. When the painting is framed, the area of the frame not covered by the painting is $108\text{ cm}^2$. What is the perimeter of the painting alone (without the frame)?
1. Let the width and height of the painting be \( w \) and \( h \) respectively.
2. The frame extends \( 3 \text{ cm} \) outward from each side, so the dimensions of the framed painting are \( w + 6 \) and \( h + 6 \).
3. The area of the framed painting is \( (w + 6)(h + 6) \).
4. The area of the painting itself is \( wh \).
5. The area of the frame alone is the difference between the area of the framed painting and the area of the painting:
   \[
   (w + 6)(h + 6) - wh = 108
   \]
6. Expanding the left-hand side:
   \[
   (w + 6)(h + 6) = wh + 6w + 6h + 36
   \]
   Therefore,
   \[
   wh + 6w + 6h + 36 - wh = 108
   \]
7. Simplifying the equation:
   \[
   6w + 6h + 36 = 108
   \]
8. Subtracting 36 from both sides:
   \[
   6w + 6h = 72
   \]
9. Dividing both sides by 6:
   \[
   w + h = 12
   \]
10. The perimeter of the painting alone is given by \( 2(w + h) \):
    \[
    2(w + h) = 2 \times 12 = 24 \text{ cm}
    \]

The final answer is \( \boxed{24 \text{ cm}} \).