"Determine end behavior" means "Find where the function going as you advance on the negative and on the positive x-axis" or equivalently "What is the behavior of the function as x -> - infinity or as x -> + infinity"
To this - we consider that as the absolute value of x goes to large numbers, every polynomial function behavior is dominated by the highest power. In this case the function f(x) -> -12x^8 as x-> - infinity or x-> + infinity
The term -12x^8 is always negative irrespective of the sign of x and goes to very large negative numbers in either x-> - infinity or x-> + infinity, case. Thus
f(x) -> - infinity on both x-> - infinity and x-> + infinity is the answer.