To find the degree, write it without exponents, like this:

3x3y4 + 5x2y3 - 4xy3

3xxxyyyy + 5xxyyy - 4xyyy

The degree is the number of letters in the longest string of letters
multiplied together.  The first term has 7 letters multiplied together,
xxxyyyy, 5 letters xxyyy are multiplied together in the 2nd term, and 
4 letters xyyy in the third term, so the degree of the polynomial is the
length of the longest string of variables multiplied together, which is 7.

[Instead of stringing the variables out you can just add the exponents.]

Edwin