Give an example of two polynomials of degree 9 whose sum has degree 4. I have no clue where to start with this. I don't know if I am supposed to make the factors cancel out.
That satisfies all the conditions doesn't it? If you want to be more complicated, make up any two 9th degree polynomials such that, when you add, all terms with power greater than 4 cancel but the terms with power 4 do not.
Your misunderstanding may have to do with thinking that factors have to cancel. That won't happen when you are adding polynomials.