To solve the expression \( -6 \frac{7}{12} - 4 \frac{1}{3} \), we first need to convert the mixed numbers into improper fractions.
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For \( -6 \frac{7}{12} \): \[ -6 \frac{7}{12} = -\left(6 \times 12 + 7\right)/12 = -\left(72 + 7\right)/12 = -\frac{79}{12} \]
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For \( -4 \frac{1}{3} \): \[ -4 \frac{1}{3} = -\left(4 \times 3 + 1\right)/3 = -\left(12 + 1\right)/3 = -\frac{13}{3} \]
Next, we will need a common denominator to add these two fractions. The denominators 12 and 3 have a least common multiple of 12.
We convert \( -\frac{13}{3} \) to have the same denominator as \( -\frac{79}{12} \): \[ -\frac{13}{3} = -\frac{13 \times 4}{3 \times 4} = -\frac{52}{12} \]
Now we can add the two fractions: \[ -\frac{79}{12} - \frac{52}{12} = -\frac{79 + 52}{12} = -\frac{131}{12} \]
Finally, we can convert \( -\frac{131}{12} \) back to a mixed number: \[ -\frac{131}{12} = -10 \frac{11}{12} \quad \text{(since } 131 \div 12 = 10 \text{ remainder } 11\text{)} \]
Therefore, the final result is: \[ -10 \frac{11}{12} \]