The mathematical expression provided in the image is:

$\frac{4(x - 3) - 2(2x - 2)}{2(3 - 4)}$

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

1. Simplify the denominator:
   $2(3 - 4) = 2(-1) = -2$

2. Expand the numerator:
   $4(x - 3) - 2(2x - 2) = 4x - 12 - 4x + 4$ Simplifying further: $4x - 4x - 12 + 4 = -8$

3. Rewrite the expression:
   $\frac{-8}{-2}$

4. Final calculation:
   $\frac{-8}{-2} = 4$

So, the result of the operation is 4.

Would you like further details on any step or have any other questions?

Here are 5 related questions:

1. What happens if we change the values inside the parentheses?
2. How does the distributive property help in simplifying such expressions?
3. Can this method be applied to more complex algebraic expressions?
4. What is the general approach for simplifying fractions involving variables?
5. How do you handle negative signs in algebraic expressions?

Tip: Always simplify the numerator and denominator separately before combining them into a single fraction!