To simplify the expression \((x-2y)(x+2y) - (x-y)^2 \cdot ((x-2y)(x+2y) - (x-y)^2)\), let's first simplify it step by step.

1. **Start with the first part**:
\[
(x-2y)(x+2y) = x^2 - (2y)^2 = x^2 - 4y^2
\]
This is the result of using the difference of squares.

2. **Next we simplify \((x - y)^2\)**:
\[
(x - y)^2 = x^2 - 2xy + y^2
\]

3. **Now inserting these into the whole expression**:
We need to substitute back into the expression:
\[
(x^2 - 4y^2) - (x^2 - 2xy + y^2)((x^2 - 4y^2) - (x^2 - 2xy + y^2))
\]

4. **Simplify \((x^2 - 4y^2) - (x^2 - 2xy + y^2)\)**:
\[
(x^2 - 4y^2) - (x^2 - 2xy + y^2) = -4y^2 + 2xy - y^2 = 2xy - 5y^2
\]

5. **Now substitute back again**:
We have:
\[
(x^2 - 4y^2) - (x^2 - 2xy + y^2)(2xy - 5y^2)
\]

6. **Now let's expand**:
Expand \((x^2 - 2xy + y^2)(2xy - 5y^2)\):
\[
= x^2(2xy - 5y^2) - 2xy(2xy - 5y^2) + y^2(2xy - 5y^2)
\]

Calculate each part:
- \(x^2(2xy - 5y^2) = 2x^3y - 5x^2y^2\)
- \(-2xy(2xy - 5y^2) = -4x^2y^2 + 10xy^3\)
- \(y^2(2xy - 5y^2) = 2xy^3 - 5y^4\)

Combining gives us:
\[
2x^3y - 5x^2y^2 - 4x^2y^2 + 10xy^3 + 2xy^3 - 5y^4 = 2x^3y - 9x^2y^2 + 12xy^3 - 5y^4
\]

7. **Putting that back into the overall expression**:
\[
(x^2 - 4y^2) - (2x^3y - 9x^2y^2 + 12xy^3 - 5y^4)
\]

Yielding:
\[
x^2 - 4y^2 - 2x^3y + 9x^2y^2 - 12xy^3 + 5y^4
\]

8. **Final Simplified Expression**:
So, the final expression simplifies to:
\[
-2x^3y + (1 + 9y^2)x^2 - 12xy^3 + (5 - 4)y^2
\]
Which can be rearranged if necessary, but this step-by-step should guide you to simplify your expression.

If you have any specific further simplifications or questions about another part of the algebra, let me know!