The expression you're asked to evaluate is:

$12^2 - (9 - 7)^3 + 6$

Let's break it down step-by-step:

1. Evaluate the exponentiation terms:
   • $12^2 = 144$
   • Inside the parentheses: $9 - 7 = 2$
   • Now, $2^3 = 8$

So, the expression simplifies to:

$144 - 8 + 6$

2. Simplify the remaining operations:
   • $144 - 8 = 136$
   • $136 + 6 = 142$

Thus, the final answer is:

$\boxed{142}$

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you calculate powers of numbers?
2. What is the order of operations (PEMDAS)?
3. How do you evaluate expressions with multiple operations?
4. How would this expression change if $9 - 7$ were squared instead of cubed?
5. How can simplifying expressions help in algebraic problem-solving?

Tip: Always remember to follow the order of operations: parentheses, exponents, multiplication/division (left to right), and addition/subtraction (left to right).