Final answer:
The question pertains to solving a non-homogeneous recurrence relation in mathematics, which requires finding solutions to the associated homogeneous equation and a particular solution to the non-homogeneous equation.
Step-by-step explanation:
To find the solution of the recurrence relation a_{n} = 8a_{n-2} - 16a_{n-4} + (-2)^n, several steps must be followed, often involving characteristic equations, generating functions, or direct computation based on initial conditions. Such problems are common in disciplines like computer science, mathematics, and engineering for analyzing algorithms, understanding numerical series, or solving difference equations.
In this case, the relation is not a standard linear homogenous recurrence relation due to the term (-2)^n, which suggests that it is a non-homogenous recurrence relation. To solve such a relation, we must typically find the general solution to the associated homogeneous equation and then find a particular solution to the non-homogeneous equation.
Given no initial conditions are provided here, a detailed solution isn't possible. However, this explanation gives a general approach to tackling such problems.