To solve for the blank in the equation \(-\frac{8}{9} \left(\frac{1}{3}\right) = -\frac{8}{__}\), we can first simplify the left side of the equation.
- Calculate \(-\frac{8}{9} \times \frac{1}{3}\): \[ -\frac{8}{9} \times \frac{1}{3} = -\frac{8 \times 1}{9 \times 3} = -\frac{8}{27} \]
Now we want to set this equal to \(-\frac{8}{__}\): \[ -\frac{8}{27} = -\frac{8}{__} \]
Since both sides have \(-8\) in the numerator, we can equate the denominators: \[ 27 = __ \]
Therefore, the blank is filled in as follows: \[ -\frac{8}{9} \left(\frac{1}{3}\right) = -\frac{8}{27} \]
Thus, the answer is: \[ 27 \]