To simplify the expression \((4 - 2x) \left(-\frac{6x^2 + 10x + 21}{4 - 2x}\right)\), we can first rewrite the expression in a way that makes it easier to work with.
Given:
\[ (4 - 2x) \left(-\frac{6x^2 + 10x + 21}{4 - 2x}\right) \]
Notice that \((4 - 2x)\) in the numerator and denominator will cancel out, assuming that \(4 - 2x \neq 0\):
\[ = - (6x^2 + 10x + 21) \]
Next, we can distribute the negative sign:
\[ = -6x^2 - 10x - 21 \]
At this point, the expression is simplified completely. Thus, the final answer is:
\[ \boxed{-6x^2 - 10x - 21} \]