To solve the expression \(-6 \frac{7}{12} - 4 \frac{1}{3}\), we will first convert both mixed numbers into improper fractions.
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Convert \(-6 \frac{7}{12}\): \[ -6 \frac{7}{12} = -\left(6 \times 12 + 7\right)/12 = -\left(72 + 7\right)/12 = -\frac{79}{12} \]
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Convert \(4 \frac{1}{3}\): \[ 4 \frac{1}{3} = 4 \times 3 + 1/3 = (12 + 1)/3 = \frac{13}{3} \]
Next, we need a common denominator to perform the subtraction. The least common multiple of 12 and 3 is 12. Therefore, we will convert \(\frac{13}{3}\) to have a denominator of 12: \[ \frac{13}{3} = \frac{13 \times 4}{3 \times 4} = \frac{52}{12} \]
Now, we can subtract the two fractions: \[
- \frac{79}{12} - \frac{52}{12} = \frac{-79 - 52}{12} = \frac{-131}{12} \]
Now, we simplify \(-\frac{131}{12}\). Since 131 is a prime number and does not share any common factors with 12 (other than 1), this fraction is already in its simplest form.
Thus, the answer is: \[ \boxed{-\frac{131}{12}} \]