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To solve the problem \(18 \frac{2}{3} - 12 \frac{1}{6}\), let's convert these mixed numbers to improper fractions:

1. **Convert \(18 \frac{2}{3}\) to an improper fraction:**
   \[
   18 \frac{2}{3} = \frac{18 \times 3 + 2}{3} = \frac{54 + 2}{3} = \frac{56}{3}
   \]

2. **Convert \(12 \frac{1}{6}\) to an improper fraction:**
   \[
   12 \frac{1}{6} = \frac{12 \times 6 + 1}{6} = \frac{72 + 1}{6} = \frac{73}{6}
   \]

3. **Find a common denominator to subtract**:
   - The least common multiple of 3 and 6 is 6.
   - Rewrite \(\frac{56}{3}\) as \(\frac{112}{6}\) (by multiplying both the numerator and denominator by 2).

4. **Subtract the fractions**:
   \[
   \frac{112}{6} - \frac{73}{6} = \frac{112 - 73}{6} = \frac{39}{6} = 6 \frac{1}{2}
   \]

So, the answer is \(6 \frac{1}{2}\), which matches the second option.

Would you like further details, or have any questions?

### Related Questions:
1. How do you convert a mixed number to an improper fraction?
2. How do you find the least common multiple of two denominators?
3. What is the process to simplify improper fractions?
4. How can mixed numbers be subtracted directly without converting them?
5. What are some real-world applications of subtracting mixed numbers?

### Tip:
Always simplify fractions after performing operations to get the answer in its simplest form.

Learn to solve the subtraction of mixed numbers: 18 2/3 - 12 1/6. This step-by-step solution explains converting mixed numbers to improper fractions, finding common denominators, and simplifying the result. Ideal for middle school students.

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