The circumference of a circle is given by the formula \( C = 2\pi r \), where \( r \) is the radius.
For circle X:
- Circumference \( C_X = 12\pi \)
- We can find the radius \( r_X \): \[ 2\pi r_X = 12\pi \] Dividing both sides by \( 2\pi \): \[ r_X = \frac{12\pi}{2\pi} = 6 \]
For circle Z:
- Circumference \( C_Z = 6\pi \)
- We can find the radius \( r_Z \): \[ 2\pi r_Z = 6\pi \] Dividing both sides by \( 2\pi \): \[ r_Z = \frac{6\pi}{2\pi} = 3 \]
Now we find the scale factor from circle X to circle Z. The scale factor can be calculated using the ratio of the radii of the two circles: \[ \text{Scale Factor} = \frac{r_Z}{r_X} = \frac{3}{6} = \frac{1}{2} \]
Thus, the scale factor from circle X to circle Z is \( 1:2 \).
So the answer is \( \boxed{1:2} \).