How do you write the polynomial so that the exponents decrease from left to right, identify the degree, and leading coefficient of the polynomial #2x^2y^2-8xy#?
That expression is already in the form desired.
When you have two or more variables, you arbitrarily pick one of them to have the decreasing exponent sequence. If they are independent, then you can also just put in alternating series.
The "degree" is reference by variable also, such as "cubic in x, and quadratic in y" if they are not the same.