The expression to evaluate from the image is:

$-4 \cdot 3 + \left( (-2)^3 - 2 \right)^2$

Step-by-step solution:

1. Simplify the exponent: $(-2)^3 = (-2) \times (-2) \times (-2) = -8$

2. Subtract 2 from the result: $-8 - 2 = -10$

3. Square the result: $(-10)^2 = 100$

4. Multiply -4 and 3: $-4 \cdot 3 = -12$

5. Add the results: $-12 + 100 = 88$

Final Answer:

$88$

Would you like more details on any specific step?

Related Questions:

1. How would the answer change if the base inside the cube was positive instead of negative?
2. How would the expression change if the exponent in $(-2)^3$ was squared instead of cubed?
3. What happens if you change the order of operations between addition and multiplication in similar expressions?
4. How would a negative exponent in $(-2)^n$ affect the final outcome?
5. What is the impact of introducing fractional exponents to similar expressions?

Tip: Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) to avoid mistakes in complex calculations.