Answer
The equation has symmetry only with respect to the x-axis.
Work Step by Step
To test for symmetry with respect to the x-axis, we substitute y for -y and check if it equals the original equation:
$2x^3-x(-y)^2=4$
$2x^3-xy^2=4 \checkmark$
To test for symmetry with respect to the y-axis, we substitute x for -x and check if it equals the original equation:
$2(-x)^3-(-x)y^2=4$
$-2x^3+xy^2=4$ nope
To test for symmetry with respect to the origin, we substitute x for -x, substitute y for -y, and check if it equals the original equation:
$2(-x)^3-(-x)(-y)^2=4$
$-2x^3+xy^2=4$ nope