-1 7/9 :(-6)

To solve \(-1 \frac{7}{9} : (-6)\), we first convert the mixed number \(-1 \frac{7}{9}\) into an improper fraction.

1. Convert \(-1 \frac{7}{9}\):

   \[ -1 \frac{7}{9} = -\left(1 \times 9 + 7\right) / 9 = -\frac{9 + 7}{9} = -\frac{16}{9} \]

2. Now, we need to divide \(-\frac{16}{9}\) by \(-6\). Dividing by a negative number is equivalent to multiplying by its reciprocal:

   \[ -\frac{16}{9} \div -6 = -\frac{16}{9} \times -\frac{1}{6} = \frac{16}{54} \]

3. Simplify \(\frac{16}{54}\):

   The greatest common divisor (GCD) of 16 and 54 is 2.

   \[ \frac{16 \div 2}{54 \div 2} = \frac{8}{27} \]

Thus, \(-1 \frac{7}{9} : (-6) = \frac{8}{27}\).