Answer
x-axis.
Work Step by Step
Step 1. To test for x-axis symmetry, replace $(x,y)$ with $(x,-y)$, we have $2(x)^3-(x)(-y)^2=4$ which is the same as the original, thus it is symmetric with respect to the x-axis.
Step 2. To test for y-axis symmetry, replace $(x,y)$ with $(-x,y)$, we have $2(-x)^3-(-x)(y)^2=4$ which is not the same as the original, thus it is not symmetric with respect to the y-axis.
Step 3. To test for origin symmetry, replace $(x,y)$ with $(-x,-y)$, we have $2(-x)^3-(-x)(-y)^2=4$ which is not the same as the original, thus it is not symmetric with respect to the origin.
