The coefficient of $$x^{-6}$$, in the expansion of $$\left(\dfrac{4x}{5} + \dfrac{5}{2x^2}\right)^9$$, is

$$\left(\frac{4x}{5} + \frac{5}{2x^2}\right)^9$$

$$T_{r+1} = {^9C_r} \left(\frac{4x}{5}\right)^{9-r} \left(\frac{5}{2x^2}\right)^r$$

$$T_{r+1} = {^9C_r} \left(\frac{4}{5}\right)^{9-r} \left(\frac{5}{2}\right)^r x^{9-3r}$$

$$9 - 3r = -6 \implies 3r = 15 \implies r = 5$$

$$\text{Coefficient} = {^9C_5} \left(\frac{4}{5}\right)^4 \left(\frac{5}{2}\right)^5$$

$$\text{Coefficient} = 126 \cdot \frac{2^8}{5^4} \cdot \frac{5^5}{2^5} = 126 \cdot 2^3 \cdot 5 = 126 \cdot 40 = 5040$$