1. **State the problem:** Evaluate the expression $$3 \cdot 4 - ((-2)^2 - 2)^3$$. 2. **Recall the order of operations:** Parentheses, exponents, multiplication/division, addition/subtraction. 3. **Calculate inside the parentheses:** $$(-2)^2 = 4$$ 4. **Substitute and simplify inside the parentheses:** $$4 - 2 = 2$$ 5. **Evaluate the cube:** $$2^3 = 8$$ 6. **Calculate the multiplication:** $$3 \cdot 4 = 12$$ 7. **Substitute back and complete the expression:** $$12 - 8 = 4$$ **Final answer:** $$4$$