To simplify the expression \(4x^2 - 3x + 7 + 2x^2 + 4x\), we can combine like terms.
First, combine the \(x^2\) terms: \[ 4x^2 + 2x^2 = 6x^2 \]
Next, combine the \(x\) terms: \[ -3x + 4x = 1x \quad \text{or simply } x \]
The constant term remains the same: \[ 7 \]
Putting it all together, we have: \[ 6x^2 + x + 7 \]
So, the simplified expression is: \[ \boxed{6x^2 + x + 7} \]