1. **State the problem:** Solve the equation $$-3\{4+2(-3x+6)\}=-2(5x-8)$$ for $x$. 2. **Apply the distributive property inside the braces:** $$-3\{4 + 2(-3x) + 2(6)\} = -2(5x - 8)$$ $$-3\{4 - 6x + 12\} = -2(5x - 8)$$ 3. **Simplify inside the braces:** $$-3\{16 - 6x\} = -2(5x - 8)$$ 4. **Distribute $-3$ on the left side:** $$-3 \times 16 + (-3) \times (-6x) = -2(5x - 8)$$ $$-48 + 18x = -2(5x - 8)$$ 5. **Distribute $-2$ on the right side:** $$-48 + 18x = -10x + 16$$ 6. **Add $10x$ to both sides to collect $x$ terms on the left:** $$-48 + 18x + 10x = -10x + 16 + 10x$$ $$-48 + 28x = 16$$ 7. **Add $48$ to both sides to isolate the term with $x$:** $$-48 + 28x + 48 = 16 + 48$$ $$28x = 64$$ 8. **Divide both sides by 28 to solve for $x$:** $$x = \frac{64}{28}$$ 9. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor 4:** $$x = \frac{\cancel{64}^{{16}}}{\cancel{28}^{{7}}}$$ 10. **Final answer:** $$x = \frac{16}{7}$$