To solve the equation \( 25(2x - 4) \cdot 12 = 0 \), we can follow these steps:

1. Recognize that the product of three factors is zero. Therefore, at least one of the factors must be zero. The factors are \( 25 \), \( (2x - 4) \), and \( 12 \).

2. Since \( 25 \) and \( 12 \) are non-zero constants, they cannot be zero. Thus, the only factor that can be zero is \( (2x - 4) \).

3. Set the factor \( (2x - 4) \) equal to zero and solve for \( x \):
\[
2x - 4 = 0
\]

4. Add 4 to both sides of the equation:
\[
2x = 4
\]

5. Divide both sides by 2:
\[
x = 2
\]

So, the solution to the equation \( 25(2x - 4) \cdot 12 = 0 \) is \( x = 2 \).