To simplify the expression \(-4a^2x \times (-2bxy) \times \left(-\frac{1}{4} x^2 y^3\right) - 4a^2x \times (-2bxy) \times \left(-\frac{1}{4} x^2 y^3\right)\), we can start with simplifying the first part of the expression:

1. **Evaluate one side of the expression**:
\[
-4a^2x \times (-2bxy) \times \left(-\frac{1}{4} x^2 y^3\right)
\]

Breaking it down:
- The first term: \(-4a^2x\)
- The second term: \(-2bxy\)
- The third term: \(-\frac{1}{4} x^2 y^3\)

Now let's multiply them together:
\[
(-4a^2x)(-2bxy)\left(-\frac{1}{4} x^2 y^3\right)
\]

Multiply the coefficients:
\[
-4 \times -2 \times -\frac{1}{4} = 2
\]

Combine the variable parts:
\[
a^2 \cdot b \cdot x \cdot y \cdot x^2 \cdot y^3 = a^2 b x^{1+2} y^{1+3} = a^2 b x^3 y^4
\]

Thus, the result of one multiplication becomes:
\[
2 a^2 b x^3 y^4
\]

2. **Now, consider the whole expression**:
Since both parts of the expression are the same, we have:
\[
2 a^2 b x^3 y^4 - 2 a^2 b x^3 y^4 = 0
\]

Thus, combining both parts we have:
\[
0
\]

The final result of the expression is:
\[
\boxed{0}
\]