To determine how long it will take Charla to complete the entire picture, we first find out how much area she can cover in one hour.
If Charla completes \(\frac{23}{12}\) of the area in 12 hours, we can calculate the area she completes in one hour by dividing this quantity by 12:
\[ \text{Area per hour} = \frac{23}{12} \div 12 = \frac{23}{12} \times \frac{1}{12} = \frac{23}{144} \]
Now, to find out how long it will take to complete 1 whole area, we take the reciprocal of her hourly rate.
The time \(t\) to complete 1 area is given by:
\[ t = \frac{1 \text{ area}}{\frac{23}{144} \text{ area per hour}} = \frac{144}{23} \text{ hours} \]
Thus, the time it will take Charla to complete the entire picture is:
\[ \boxed{\frac{144}{23}} \text{ hours} \]