To simplify the expression \( 4x^2 - 12x + 24x \), you first combine like terms.
The terms \(-12x\) and \(24x\) can be combined:
\[ -12x + 24x = 12x \]
Now, substitute this back into the expression:
\[ 4x^2 + 12x \]
Now, you can write it in standard form, which is organized by the degree of the terms (with the highest degree first):
\[ 4x^2 + 12x \]
Therefore, the simplified expression in standard form is:
\[ \boxed{4x^2 + 12x} \]