xy8 + 7x8y2 - 6xy4 + 2

The degree of a term is the number of letters multiplied together
when the term is written without exponents.  

Its coefficient is the number that's multiplied by the letters, or if
there are no letters multiplied, it is just the term itself.  
(understood)


Write all the terms without exponents:

xyyyyyyyy + 7xxxxxxxxyy - 6xyyyy + 2

The first term xyyyyyyyy contains the product of 9 letters, so its degree is 9.
Its coefficient is 1 (understood).

The second term 7xxxxxxxxyy contains the product of 10 letters, so its degree
is 10.  Its coefficient is 7

The third term -6xyyyy contains the product of 5 letters, so its degree is 5.
Its coefficient is -6

The fourth term 2 contains the product of 0 letters, so its degree is 0.
Its coefficient is 2 

The degree of the whole polynomial is the same as the degree of its term
with the largest degree.  So the degree of the whole polynomial is 10.

Edwin