The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

For '12w^3 x^5 v^3 +3+4x^12+vw^4' the degrees of its monomials are:

12w^3 x^5 v^3 has degree 3 + 5 + 3 = 11

3 has degree 0

4x^12 has degree 12

vw^4 has degree 1 + 4 = 5

The degree of '12w^3 x^5 v^3 +3+4x^12+vw^4'  is 12.