1. State the problem: Determine which of the given choices is not in the interval $-\tfrac{1}{2} < x < \tfrac{2}{3}$. 2. Interpretation and method: A number is in the interval if it is greater than $-\tfrac{1}{2}$ and less than $\tfrac{2}{3}$. 3. Test A) $-1$. Since $-1 < -\tfrac{1}{2}$, $-1$ is not in the interval. 4. Test B) $\tfrac{1}{2}$. $\tfrac{1}{2}=0.5$ and $-\tfrac{1}{2} < \tfrac{1}{2} < \tfrac{2}{3}$, so $\tfrac{1}{2}$ is in the interval. 5. Test C) $12$. $12$ is greater than $\tfrac{2}{3}$, so $12$ is not in the interval. 6. Test D) $\tfrac{1}{4}$. $\tfrac{1}{4}=0.25$ and $-\tfrac{1}{2} < \tfrac{1}{4} < \tfrac{2}{3}$, so $\tfrac{1}{4}$ is in the interval. 7. Conclusion: The choices not in the interval are A) $-1$ and C) $12$. Final answer: A and C.