To simplify the expression \( 12 - 2\sqrt{512} - 2\sqrt{5} \), we need to first simplify \( \sqrt{512} \).

1. **Simplifying \( \sqrt{512} \)**:
\[
512 = 256 \times 2 = 16^2 \times 2
\]
Thus,
\[
\sqrt{512} = \sqrt{256 \cdot 2} = \sqrt{256} \cdot \sqrt{2} = 16\sqrt{2}
\]

2. **Substituting back into the expression**:
Now, we can substitute for \( \sqrt{512} \):
\[
12 - 2\sqrt{512} - 2\sqrt{5} = 12 - 2(16\sqrt{2}) - 2\sqrt{5}
\]
This simplifies to:
\[
12 - 32\sqrt{2} - 2\sqrt{5}
\]

3. **Final expression**:
Therefore, the expression simplifies to:
\[
12 - 32\sqrt{2} - 2\sqrt{5}
\]

This is the simplified form of the given expression.