1. Stating the problem: Simplify the expression $-3[2 - (5 - 4) + (-6)] + 7 - (-2 \cdot 3)$. 2. Simplify inside the parentheses: Calculate $(5 - 4) = 1$. 3. Substitute back: $-3[2 - 1 + (-6)] + 7 - (-2 \cdot 3)$. 4. Simplify inside the brackets: $2 - 1 = 1$, so $1 + (-6) = 1 - 6 = -5$. 5. Expression becomes: $-3[-5] + 7 - (-2 \cdot 3)$. 6. Multiply: $-3 \times -5 = 15$. 7. Calculate $-2 \cdot 3 = -6$, so $-(-6) = +6$. 8. Expression is now: $15 + 7 + 6$. 9. Add all terms: $15 + 7 = 22$, then $22 + 6 = 28$. 10. Final answer: $28$.