1. **State the problem:** Simplify the expression $$3(6x^{-9} y^{7} z^{2}) - 3xy^{5} 8x^{2} z^{-3} y^{2} - 3xy^{5} 8x^{2} z^{-3} y^{2}$$. 2. **Rewrite the expression:** $$3 \times 6x^{-9} y^{7} z^{2} - 3xy^{5} \times 8x^{2} z^{-3} y^{2} - 3xy^{5} \times 8x^{2} z^{-3} y^{2}$$ 3. **Multiply constants and combine like terms:** $$18x^{-9} y^{7} z^{2} - 24x^{3} y^{7} z^{-3} - 24x^{3} y^{7} z^{-3}$$ 4. **Combine the like terms in the subtraction:** $$18x^{-9} y^{7} z^{2} - (24x^{3} y^{7} z^{-3} + 24x^{3} y^{7} z^{-3})$$ 5. **Add the like terms:** $$18x^{-9} y^{7} z^{2} - 48x^{3} y^{7} z^{-3}$$ 6. **Final simplified expression:** $$\boxed{18x^{-9} y^{7} z^{2} - 48x^{3} y^{7} z^{-3}}$$