To solve the system of equations given:

1. \( |2x - 3y| + \sqrt{4xy} + 25z^2 = 6 \)
2. \( x + y + z = 33 \)

Let's proceed with solving:

Start by addressing the absolute value and square root in Equation 1. These can complicate the algebraic manipulation, so consider different cases for \( |2x - 3y| \). Furthermore, since we're solving for three variables and have only two equations, expect potentially infinite solutions or more conditions needed.

### Steps for an Example Solution:

1. **Express one variable in terms of others** using Equation 2:

\[
z = 33 - x - y
\]

2. **Substitute \( z \) into Equation 1**:

\[
|2x - 3y| + \sqrt{4xy} + 25(33 - x - y)^2 = 6
\]

3. **Solve the equation iteratively or using assumptions**: You might simplify by trying integer values for \( x \) or \( y \), checking if a solution is viable.

4. **Evaluate the system for different cases**: Given the complexity, numeric solutions or programming methods (e.g., Python, MATLAB) can efficiently find solutions.

5. **Check solution works in both equations**: Any found set of solutions must satisfy both equations.

Without specific numbers or further constraints, expressing \( y \) and \( x \) might require trial and error or numerical computation for possible solutions that fit both equations.