To simplify the expression $\frac{1}{2}+\{4\frac{3}{4}-(3\frac{1}{6}-2\frac{1}{3})\}$, follow these steps:

1. Calculate $3\frac{1}{6}-2\frac{1}{3}$:

First, convert the mixed numbers to improper fractions:
$$3\frac{1}{6}=\frac{19}{6}$$
$$2\frac{1}{3}=\frac{7}{3}$$

Find a common denominator for $\frac{19}{6}$ and $\frac{7}{3}$. The least common denominator is 6:
$$\frac{7}{3}=\frac{14}{6}$$

Now subtract:
$$\frac{19}{6}-\frac{14}{6}=\frac{5}{6}$$

2. Subtract the result from $4\frac{3}{4}$:

Convert $4\frac{3}{4}$ to an improper fraction:
$$4\frac{3}{4}=\frac{19}{4}$$

Convert $\frac{5}{6}$ to a fraction with denominator 4:
$$\frac{5}{6}=\frac{10}{12}\text{ (Equivalent fraction)}$$
$$\frac{5}{6}=\frac{5}{6}=\frac{10}{12}=\frac{10}{12}=\frac{10}{12}=\frac{5}{6}=\frac{5}{6}=\frac{10}{12}$$

Now subtract:
$$\frac{19}{4}-\frac{5}{6}$$
Find a common denominator, which is 12:
$$\frac{19}{4}=\frac{57}{12}$$
$$\frac{5}{6}=\frac{10}{12}$$
Subtract:
$$\frac{57}{12}-\frac{10}{12}=\frac{47}{12}$$

3. Add $\frac{1}{2}$ to $\frac{47}{12}$:

Convert $\frac{1}{2}$ to a fraction with denominator 12:
$$\frac{1}{2}=\frac{6}{12}$$

Add:
$$\frac{47}{12}+\frac{6}{12}=\frac{53}{12}$$

Convert $\frac{53}{12}$ to a mixed number:
$$\frac{53}{12}=4\frac{5}{12}$$


The final result is $4\frac{5}{12}$.

The correct answer is C. 4 \frac{5}{12}.