If I understood your question correctly, you are saying that the degree of a term should be the maximum degree between the vatiables in that term. So (a^2)(b^1)(c^4) ) would be of degree max(2,1,4) = 4.
But with the definition he is using, the degree of a term in the equation is the sum of the degrees of the variables. So (a^2)(b^1)(c^4) has degree 2 + 1 + 4 = 7.
I don't think that's right. See the sibling comment, which made it click for me. He is saying the degree of a single term is the sum of the exponents in that term, and the degree of the equation is max(...all term degrees).
But with the definition he is using, the degree of a term in the equation is the sum of the degrees of the variables. So (a^2)(b^1)(c^4) has degree 2 + 1 + 4 = 7.