-6x²y + 4xy – 7y

Get rid of the exponents by writing the square x² as the product
of x and x.

-6xxy + 4xy - 7y

Now count the number of letters multiplied by the coefficient in 
each of the three terms:


-6xxy  has a row of 3 letters multiplied by the coefficient -6,
so that term has degree 3.


+4xy  has a row of 2 letters multiplied by the coefficient +4,
so that term has degree 2.


-7y has just one letter multiplied by the coefficient -7, 
so that term has degree 1.

Now whichever term has the largest degree, we take that to 
be the degree of the ENTIRE polynomial.  So since the first 
term has the largest degree, which is 3, the whole polynomial 
has that same degree, which is 3.

In a nutshell, the degree of a polynomial is the most number 
of letters multiplied together by the coefficient in any of its 
terms.  An exponent is considered to be a string of the same 
letter repeated to be multiplied the same number of times as the 
exponent.  

The longest string of letters in any of the three terms is 3,
so the polynomial, which is called a "trinomial" because it 
has three terms, has degree 3.

But don't get those mixed up just because they're both 3.  It's
a trinomial because it has three terms, but it has degree 3 
because the first term has the most number of letters 
multiplied together by the coefficient, which is 3 letters.

Edwin