How do I solve? Or what is the answer for this?

Notice that the square root is accompanied with ^2 and can be simplified:
This works because 4x^4 = (2x^2)^2
[tex]\sqrt{(2x^{2})^{2} * (256y^{8})^{2} }[/tex]
Remove the square root:
[tex]2x^{2} (256y^{8} )[/tex]
Calculate the product:
[tex]512x^{2} y^{8}[/tex]
This is your answer after simplification.