Find $f_x$ and $f_y$
$$f(x,y)=-6e^{5x-4y}$$

Step 1 ：The function given is $f(x,y)=-6e^{5x-4y}$. We are asked to find the partial derivatives of this function with respect to $x$ and $y$.

Step 2 ：The partial derivative of a function with respect to a variable is the derivative of the function with respect to that variable, treating all other variables as constants.

Step 3 ：For $f_x$, we differentiate $f(x,y)$ with respect to $x$, treating $y$ as a constant. The derivative of $e^{ax}$ with respect to $x$ is $a{e}^{ax}$, so $f_x=-30e^{5x-4y}$.

Step 4 ：For $f_y$, we differentiate $f(x,y)$ with respect to $y$, treating $x$ as a constant. The derivative of $e^{ax}$ with respect to $x$ is $a{e}^{ax}$, so $f_y=24e^{5x-4y}$.

Step 5 ：Final Answer: The partial derivative of $f(x,y)=-6e^{5x-4y}$ with respect to $x$ is $f_x=-30e^{5x-4y}$ and with respect to $y$ is $f_y=24e^{5x-4y}$. So, the final answer is $\boxed{{\displaystyle f_x=-30e^{5x-4y},f_y=24e^{5x-4y}}}$.