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To solve and estimate \( 4 \frac{2}{3} + 6 \frac{7}{8} \), let's break it down step by step:

### Step 1: Estimate the Mixed Numbers
We have two mixed numbers:
- \( 4 \frac{2}{3} \)
- \( 6 \frac{7}{8} \)

We can round these fractions for easier estimation:
- \( \frac{2}{3} \) is close to 1, so we approximate \( 4 \frac{2}{3} \) as 5.
- \( \frac{7}{8} \) is very close to 1, so we approximate \( 6 \frac{7}{8} \) as 7.

### Step 2: Add the Approximated Values
Now, we add the two approximations:
\[
5 + 7 = 12
\]

### Conclusion:
The best estimate for \( 4 \frac{2}{3} + 6 \frac{7}{8} \) is approximately **12**. Thus, the correct answer is **C: 12**.

Do you want more detailed steps or have any other questions?

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Here are five related questions to expand your understanding:
1. How would you add these mixed numbers without estimating?
2. What is the process for converting mixed numbers into improper fractions?
3. Can you think of a situation where rounding might lead to an incorrect estimate?
4. What are some ways to add fractions with different denominators?
5. How can we verify if an estimate is close to the exact answer?

**Tip**: When estimating, it's useful to round fractions to the nearest half or whole number for quicker calculations!

Learn how to estimate the sum of mixed numbers, such as 4 2/3 + 6 7/8, by rounding the fractions and adding the whole numbers. This problem introduces key concepts in fraction estimation for students in Grades 4-6.

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