The coefficient of $x^{-4}$in ${(2x-\frac{3}{x})}^8$is 

General term ${(a+b)}^n$

$t_{r+1}={}^n{\text{C}}_r{a}^{n-r}{b}^r$

$t_{r+1}={}^8{\text{C}}_r{\left(2x\right)}^{8-r}{\left(\frac{-3}{x}\right)}^r$

$={}^8{\text{C}}_r{2}^{8-r}.x^{8-r}.\frac{{(-3)}^r}{x^r}$

$={}^8{\text{C}}_r{2}^{8-r}{(-3)}^r.x^{8-2r}$

$x^{-4}$ co-efficient

$8-2r=-4$

$12=2r$

$r=6$

$t_7={}^8{\text{C}}_6{2}^{8-6}{(-3)}^6$

$t_7={}^8{\text{C}}_6{.2}^2{.3}^6$