Let's break down the expression step by step:

Given expression: $4(1 + 8 \cdot 6) - 6^2$

1. Evaluate inside the parentheses: $8 \cdot 6 = 48$ So, the expression inside the parentheses becomes: $1 + 48 = 49$

2. Multiply by 4: $4 \cdot 49 = 196$

3. Evaluate the exponent: $6^2 = 36$

4. Subtract: $196 - 36 = 160$

So, the final result is 160.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would the expression change if the exponent were $6^3$ instead?
2. What happens if the multiplication sign in the parentheses is replaced by addition?
3. How do you evaluate $4(2 + 7 \cdot 5) - 3^2$?
4. How would the expression evaluate if there were a division by 2 after the subtraction?
5. What is the result if you change the 4 to an 8 in the expression?

Tip: Always remember the order of operations, often remembered by PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).