We can factor $w^4 - 16$ as $(w^2 - 4)(w^2 + 4)$.
Note that $(w^2 - 4)$ can be further factored as $(w - 2)(w + 2)$.
However, $(w^2 + 4)$ cannot be further factored using monic polynomials with real coefficients.
Therefore, the maximum possible factorization of $w^4 - 16$ using monic polynomials with real coefficients is $(w - 2)(w + 2)(w^2 + 4)$.
The answer is: (w-2)(w+2)(w^2+4)
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the maximum possible factorization of $w^4 - 16$ using monic polynomials with real coefficients?

### Answer:
