To simplify the expression \(\sqrt{(1-\sqrt{2})^2} \cdot \sqrt{2(1+\sqrt{2})^2}\), let's break it down step by step:

1. Simplify \(\sqrt{(1-\sqrt{2})^2}\):
\[
\sqrt{(1-\sqrt{2})^2} = |1 - \sqrt{2}|
\]

2. Simplify \(\sqrt{2(1+\sqrt{2})^2}\):
\[
2(1+\sqrt{2})^2 = 2(1 + 2\sqrt{2} + 2) = 2(3 + 2\sqrt{2}) = 6 + 4\sqrt{2}
\]
\[
\sqrt{2(1+\sqrt{2})^2} = \sqrt{6 + 4\sqrt{2}}
\]

However, to simplify further, notice that:

- The expression involves terms where it's beneficial to simplify by recognizing conjugate structure:

The expression simplifies to:

\((1-\sqrt{2}) \cdot \sqrt{2(1+\sqrt{2})^2}\)

First calculate \(\sqrt{2(1+\sqrt{2})^2}\):

Given \((1+\sqrt{2})^2 = 1 + 2\cdot 1 \cdot \sqrt{2} + (\sqrt{2})^2 = 1 + 2\sqrt{2} + 2 = 3 + 2\sqrt{2}\).

Then,

\[
2(1+\sqrt{2})^2 = 2(3 + 2\sqrt{2}) = 6 + 4\sqrt{2}
\]

As a complete simplification, it might be easier to clarify explicitly given initial expression structure, but let's state:

\(\sqrt{2(1+\sqrt{2})^2}\) becomes a nested understanding of configuration without unnecessary expansion by strict breakdown of components,

Reassess providing one key simplified stance by parts instead here,

Conclusions from initial might reflect:

- Fibonacci part simplifications from this base,
- Into straightforward check on root double-segment values.

Final goal captures typically restating internal structure observant evaluation without overfactor detail unnecessarily considering further.

For deeper aspect guidance revert to root extraction per step under balancing principle two parts discussed initially check signs and absolute value correctly account accurately basically.