We can start by simplifying the numerator and the denominator separately.
The square root of 128 can be written as the square root of 64 times 2, which simplifies to 8 times the square root of 2.
The denominator can be simplified using the difference of squares formula:
\begin{align*}
\sqrt{32} - 2\sqrt{2} &= \sqrt{16 \times 2} - 2\sqrt{2} \\
&= 4\sqrt{2} - 2\sqrt{2} \\
&= 2\sqrt{2}
\end{align*}
Now we can substitute these simplifications back into the original expression:
\begin{align*}
\frac{\sqrt{128}}{\sqrt{32} - 2\sqrt{2}} &= \frac{8\sqrt{2}}{2\sqrt{2}} \\
&= 4
\end{align*}
Therefore, the simplified expression is 4.