Final answer:
The degree of the polynomial is 4.
Step-by-step explanation:
The given polynomial is 3 - 8u²w⁴ + 2-vu? + 4w.
To find the degree of the polynomial, we need to determine the highest power of the variables.
In this case, the highest power is 4, which corresponds to the term -8u²w⁴.
Therefore, the degree of the polynomial is 4.