Answer
symmetric with respect to the $y$-axis.
Work Step by Step
1. Replace $(x,y)$ with $(x,-y)$ ($x$-axis symmetry), we have $(x)^2+(-y)^3=2(x)^4$ which is different from the original, thus it is not symmetric with respect to the $x$-axis.
2. Replace $(x,y)$ with $(-x,y)$ ($y$-axis symmetry), we have $(-x)^2+(y)^3=2(-x)^4$ which is no different from the original, thus it is symmetric with respect to the $y$-axis.
3. Replace $(x,y)$ with $(-x,-y)$ (origin symmetry), we have $(-x)^2+(-y)^3=2(-x)^4$ which is different from the original, thus it is not symmetric with respect to the origin.
