$\text{Two curves }{C}_1\equiv {\left[f\left(y\right)\right]}^{2/3}+{\left[f\left(x\right)\right]}^{1/3}=0\text{and}{C}_2\equiv {\left[f\left(y\right)\right]}^{2/3}+{\left[f\left(x\right)\right]}^{2/3}=12,\text{ satisfying the relation }\left(x-y\right)f\left(x+y\right)-\left(x+y\right)f\left(x-y\right)=4xy\left(x^2-y^2\right)$
The area bounded by $C_1\text{and}{C}_2$ is

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