When finding the degree of a multivariable polynomial, remember to keep your head above ground. That goes for any ostriches who may be reading this. Ignore the constants and look for the exponents hovering in superscript. To find the degree of a multivariable term, add together the exponents of all the variables in that term. Isn't it nice to be asked to add once in a while?
You already know that the degree of a polynomial is the largest degree of any of its terms. Well, guess what? The same is true for multivariable polynomials. To see which term has the largest degree, we need to find the degree of each of the terms and then pick the biggest number. "Picking the biggest of something" is about the only thing easier than adding, so you should have no problems here.