To simplify the expression \( 2x + \frac{\pi}{4} + \frac{4x}{2} \), we can first simplify the term \( \frac{4x}{2} \):
\[ \frac{4x}{2} = 2x \]
Now, we can rewrite the entire expression:
\[ 2x + \frac{\pi}{4} + 2x \]
Next, combine the \( 2x \) terms:
\[ 2x + 2x = 4x \]
So, the expression simplifies to:
\[ 4x + \frac{\pi}{4} \]
Therefore, the final simplified expression is:
\[ 4x + \frac{\pi}{4} \]