1. **State the problem:** Simplify the expression $2 \cdot [8 - 3(4 + 2)] - 3$. 2. **Apply the order of operations (PEMDAS):** Parentheses first, then multiplication, then addition/subtraction. 3. **Calculate inside the parentheses:** $$4 + 2 = 6$$ 4. **Multiply inside the brackets:** $$3 \times 6 = 18$$ 5. **Substitute back into the expression:** $$2 \cdot [8 - 18] - 3$$ 6. **Simplify inside the brackets:** $$8 - 18 = -10$$ 7. **Multiply:** $$2 \times (-10) = -20$$ 8. **Subtract:** $$-20 - 3 = -23$$ **Final answer:** $-23$