Let's break down the mathematical expression from the image step by step. The expression is:

$2 \cdot 4^2 - 8 \div 2 \cdot (5+2) \cdot 2$

Step 1: Evaluate exponents

$4^2 = 16$

Now the expression becomes: $2 \cdot 16 - 8 \div 2 \cdot (5+2) \cdot 2$

Step 2: Simplify the parentheses

$(5+2) = 7$

Now the expression becomes: $2 \cdot 16 - 8 \div 2 \cdot 7 \cdot 2$

Step 3: Perform division and multiplication from left to right

First, perform $8 \div 2 = 4$:

$2 \cdot 16 - 4 \cdot 7 \cdot 2$

Next, perform $4 \cdot 7 = 28$:

$2 \cdot 16 - 28 \cdot 2$

Next, perform $28 \cdot 2 = 56$:

$2 \cdot 16 - 56$

Next, perform $2 \cdot 16 = 32$:

$32 - 56$

Step 4: Subtract

$32 - 56 = -24$

Thus, the final result of the expression is: $\boxed{-24}$

Would you like further details or explanations on any step? Here are some related questions to consider:

1. How do you determine the order of operations (PEMDAS)?
2. What happens if the parentheses in the expression are moved?
3. Can you solve similar expressions with different exponents?
4. What is the impact of division and multiplication order in expressions?
5. How can you simplify complex arithmetic expressions efficiently?

Tip: Always remember to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) to avoid calculation errors.