1. Problem: Calculate the value of $l = \left|\left(\frac{8}{3} - 8\right) - \left(-\frac{8}{3} + 8\right)\right|$. 2. First, simplify inside the absolute value step by step. 3. Calculate $\frac{8}{3} - 8$: $$\frac{8}{3} - 8 = \frac{8}{3} - \frac{24}{3} = \frac{8 - 24}{3} = \frac{-16}{3}$$ 4. Calculate $-\frac{8}{3} + 8$: $$-\frac{8}{3} + 8 = -\frac{8}{3} + \frac{24}{3} = \frac{-8 + 24}{3} = \frac{16}{3}$$ 5. Substitute back into the expression: $$l = \left| \frac{-16}{3} - \frac{16}{3} \right|$$ 6. Combine the terms inside the absolute value: $$l = \left| \frac{-16}{3} - \frac{16}{3} \right| = \left| \frac{-16 - 16}{3} \right| = \left| \frac{-32}{3} \right|$$ 7. The absolute value of a negative fraction is its positive counterpart: $$l = \frac{32}{3}$$ 8. Final answer: $$l = \frac{32}{3}$$