at what displacement potential ewnergy is one 4^th of its maximum value?

 

Since it isn’t mentioned where but the question is likely to be of SHM so,

Let the amplitude is A
Potential Energy will be maximum when displacement is maximum from the mean position i.e A.
Potential Energy when x=A, U=kA²/2

ATQ,
kA²/8 = kx²/2
=>x=A/2.