To subtract the mixed numbers \(-4 \frac{5}{11}\) and \(2 \frac{4}{11}\), we can first convert them into improper fractions.
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Convert \(-4 \frac{5}{11}\) to an improper fraction: \[ -4 \frac{5}{11} = -\left(4 \cdot 11 + 5\right)/11 = -\left(44 + 5\right)/11 = -\frac{49}{11} \]
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Convert \(2 \frac{4}{11}\) to an improper fraction: \[ 2 \frac{4}{11} = 2 \cdot 11 + 4/11 = (22 + 4)/11 = \frac{26}{11} \]
Now we can perform the subtraction: \[ -\frac{49}{11} - \frac{26}{11} = -\left(\frac{49 + 26}{11}\right) = -\frac{75}{11} \]
Finally, we can convert \(-\frac{75}{11}\) back into a mixed number: \[ -\frac{75}{11} = -6 \frac{9}{11} \] (since \(75 \div 11 = 6\) with a remainder of \(9\)).
Thus, the answer is: \[ -6 \frac{9}{11} \]