By the binomial theorem,
[tex](2x^3-3x)^9=\displaystyle\sum_{k=0}^9\binom9k(2x^3)^{9-k}(-3x)^k=2^9\sum_{k=0}^9\binom9k \left(-\frac32\right)^k x^{27-2k}[/tex]
where
[tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]
is the binomial coefficient.
The x¹⁹ terms occurs for 27 - 2k = 19, or k = 4, which has coefficient
[tex]2^9\dbinom94\left(-\dfrac32\right)^4=\boxed{326,592}[/tex]
