1. **State the problem:** Simplify the expression $$\frac{8a}{9c} - \frac{64a^2 + 81c^2}{72ac} + \frac{9c - 64a}{8a}.$$\n\n2. **Identify the common denominator:** The denominators are $9c$, $72ac$, and $8a$. The least common denominator (LCD) is $72ac$ because $72ac$ is divisible by $9c$ and $8a$.\n\n3. **Rewrite each term with the LCD:**\n- First term: $$\frac{8a}{9c} = \frac{8a \times 8a}{9c \times 8a} = \frac{64a^2}{72ac}.$$\n- Second term is already over $72ac$.\n- Third term: $$\frac{9c - 64a}{8a} = \frac{(9c - 64a) \times 9c}{8a \times 9c} = \frac{81c^2 - 576ac}{72ac}.$$\n\n4. **Combine all terms over the common denominator:**\n$$\frac{64a^2}{72ac} - \frac{64a^2 + 81c^2}{72ac} + \frac{81c^2 - 576ac}{72ac} = \frac{64a^2 - (64a^2 + 81c^2) + 81c^2 - 576ac}{72ac}.$$\n\n5. **Simplify the numerator:**\n$$64a^2 - 64a^2 - 81c^2 + 81c^2 - 576ac = -576ac.$$\n\n6. **Final simplified expression:**\n$$\frac{-576ac}{72ac} = -8.$$\n\n**Answer:** The expression simplifies to $-8$.