${\mathit{x}}^2{\left(\frac{{\mathit{d}}^2\mathit{y}}{\mathit{d}{\mathit{x}}^2}\right)}^2+{\left(\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}}\right)}^4$ = 0
We know that the degree of a differential equation is the highest power (exponent) of the highest order derivative in it.
The highest order derivative present in the given differential equation is $\frac{{\mathit{d}}^2\mathit{y}}{\mathit{d}{\mathit{x}}^2}$. Its power is 2. So, the degree of the given differential equation is 2.