If point C is placed using point B as an endpoint of the copy of segment \( \overline{AB} \), then \( AC \) is equal to \( AB \) plus another \( AB \).
The measure of segment \( \overline{AB} \) is given as 22.3 millimeters. Therefore, the measure of segment \( \overline{AC} \) would be:
\[
AC = AB + AB = 22.3 \, \text{mm} + 22.3 \, \text{mm} = 44.6 \, \text{mm}
\]
Thus, the correct response is:
**The measure of \( \overline{AC} \) is 44.6 millimeters.**