Replace x with -x.
Even: f(x) = f(-x) and Odd: -f(x) = f(-x)
6(-x)*|2(-x)^3)| = -6x*|2x^3|: Absolute value is always positive, so the negative sign inside the absolute value drops.
6(-x)*|2(-x)^3)| = -f(x) (the whole function multiplied by -1). So it's an odd function.
You can check this easily by substituting 1 in for x. Compare it to using -1 for x, and 1 then multiplying the answer by -1.
f(1) = 6*1*|2*1^3| = 6*2 = 12
f(-1) = 6*(-1)*|2*(-1)^3| = -6*|-2| = -6*2 = -12
-f(1) = -12 = f(-1): Odd function.
You can also verify it by graphing the function. If the values on the left side of the y-acis (the values for -x's) are the same as the values on the right side, it is even. For example, the graph is at the same point when x=1 and when x=-1, x=2 and x=-2 etc.
If the values on the left side (positive x values) are opposites of the graph's values for the corresponding negative x values, then it's an odd function. For example when x=1 the graph is at (1,3), and when x = -1 the graph is at (-1,-3); (2,4), (-2,-4) etc.
(