1. example of fourth-degree trinomial
2. example of cubic polynomial with four terms

So, i think all you really need here is some definitions:
degree is the highest exponent that a polynomial has; a "fourth-degree" polynomial would have a highest exponent of 4.
a trinomial is a polynomial with 3 terms (tri means 3).
a cubic polynomial is a polynomial with an exponent of three.
terms are the values separated by signs in a polynomial; for example, in the binomial x - 1, both "x" and "-1" are terms.

with that info, an example of a fourth-degree trinomial is simply one with an exponent of 4 and 3 total terms: x⁴ + x² + 16 is one example, but there are mny examples you could create from it. x⁴ + x + 1 has a degree of 4 and three terms, so you can do whatever you want with it.

an example of a cubic polynomial with 4 terms could be x³ + x² + x + 1; x³ + 2x² + 27x + 119 is another. the most important thing for this one is that you list out x³, x², and x as well as a constant, because that's the only way to secure their placement in the polynomial without becoming like terms that combine and turn into fewer terms. you couldn't put two x² terms or multiple constants because they simplify into a single term.