1. The problem is to subtract the mixed numbers $6 \frac{2}{12}$ and $-2 \frac{5}{10}$. 2. First, convert the mixed numbers to improper fractions. For $6 \frac{2}{12}$: $$6 \frac{2}{12} = 6 + \frac{2}{12} = \frac{6 \times 12}{12} + \frac{2}{12} = \frac{72}{12} + \frac{2}{12} = \frac{74}{12}$$ For $-2 \frac{5}{10}$: $$-2 \frac{5}{10} = -\left(2 + \frac{5}{10}\right) = -\left(\frac{20}{10} + \frac{5}{10}\right) = -\frac{25}{10}$$ 3. To subtract, write the expression as: $$\frac{74}{12} - \left(-\frac{25}{10}\right) = \frac{74}{12} + \frac{25}{10}$$ 4. Find a common denominator for $12$ and $10$, which is $60$. Convert fractions: $$\frac{74}{12} = \frac{74 \times 5}{12 \times 5} = \frac{370}{60}$$ $$\frac{25}{10} = \frac{25 \times 6}{10 \times 6} = \frac{150}{60}$$ 5. Add the fractions: $$\frac{370}{60} + \frac{150}{60} = \frac{520}{60}$$ 6. Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is $20$: $$\frac{520 \div 20}{60 \div 20} = \frac{26}{3}$$ 7. Convert the improper fraction back to a mixed number: $$\frac{26}{3} = 8 \frac{2}{3}$$ Final answer: $8 \frac{2}{3}$