Answer
even.
Work Step by Step
Step 1. Replace $x$ with $-x$, we have $f(-x)=0.5(-x)^4-2(-x)^2+6=0.5(x)^4-2(x)^2+6= f(x)$, thus it is even.
Step 2. Replace $x$ with $-x$, we have $f(-x)=0.5(-x)^4-2(-x)^2+6=0.5(x)^4-2(x)^2+6\ne-f(x)$, thus it is not odd.