To subtract the mixed numbers \(-6 \frac{7}{12}\) and \(-4 \frac{1}{3}\), we first convert them to improper fractions.
- Convert \(-6 \frac{7}{12}\):
\[ -6 \frac{7}{12} = -\left(6 \times 12 + 7\right)/12 = -\left(72 + 7\right)/12 = -\frac{79}{12} \]
- Convert \(-4 \frac{1}{3}\):
\[ -4 \frac{1}{3} = -\left(4 \times 3 + 1\right)/3 = -\left(12 + 1\right)/3 = -\frac{13}{3} \]
Now we need a common denominator to subtract these fractions. The least common multiple of 12 and 3 is 12. Convert \(-\frac{13}{3}\) to a fraction with a denominator of 12:
\[ -\frac{13}{3} = -\frac{13 \times 4}{3 \times 4} = -\frac{52}{12} \]
Now we can subtract the two fractions:
\[ -\frac{79}{12} - \left(-\frac{52}{12}\right) = -\frac{79}{12} + \frac{52}{12} = \frac{52 - 79}{12} = -\frac{27}{12} \]
We can simplify \(-\frac{27}{12}\):
\[ -\frac{27}{12} = -\frac{9}{4} \quad (\text{by dividing the numerator and denominator by 3}) \]
Now, convert \(-\frac{9}{4}\) back to a mixed number:
\[ -\frac{9}{4} = -2 \frac{1}{4} \]
Thus, the final answer is:
\[ -2 \frac{1}{4} \]