1. **State the problem:** Find what is $6 \frac{4}{5}\%$ of 33. 2. **Convert the mixed number percent to an improper fraction:** $$6 \frac{4}{5}\% = \left(6 + \frac{4}{5}\right)\% = \frac{30}{5} + \frac{4}{5} = \frac{34}{5}\%$$ 3. **Convert the percent to a decimal or fraction:** Percent means per hundred, so: $$6 \frac{4}{5}\% = \frac{34}{5} \times \frac{1}{100} = \frac{34}{500} = \frac{17}{250}$$ 4. **Calculate $\frac{17}{250}$ of 33:** $$33 \times \frac{17}{250} = \frac{33 \times 17}{250} = \frac{561}{250}$$ 5. **Simplify or convert to decimal:** $$\frac{561}{250} = 2.244$$ **Answer:** $6 \frac{4}{5}\%$ of 33 is $\boxed{2.244}$.