Question 413036
Check out this reference for a fuller explanation of degree of a polynomial.  


<a href = "http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut25_poly.htm" target = "_blank">http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut25_poly.htm</a>


your polynomial is equal to -6x^3+4x^2+3x+4 


The degree of the first term is 3
The degree of the second term is 2
The degree of the third term is 1
The degree of the last term is 0


Since the term with the highest sum of exponents is the first term, the degree of the polynomial is 3.


Sum of exponents applies to when you have more than 1 variable in a term


x^3 is a term with a degree of 3.
x^3*y^2 is a term with a degree of 5.


Check out the reference.  It explains it well.