What is the coefficient of $x^2y^6$ in the expansion of $\left(\frac{3}{5}x-\frac{y}{2}\right)^8$?  Express your answer as a common fraction.
By the Binomial theorem, this term is $$\binom82 \left(\frac{3}{5}x\right)^2\left(-\frac{y}{2}\right)^6=28\cdot\frac{9}{25}\cdot\frac{1}{64}x^2y^6=\boxed{\frac{63}{400}}x^2y^6$$