\(W _{\text {net }}=\left( K _{ f }- K _{ i }\right)\)

\(\Rightarrow-\frac{1}{2} Kx ^{2}=\frac{1}{2} m \left(\frac{ v }{2}\right)^{2}-\frac{1}{2} mv ^{2}=\frac{ E }{4}- E\)

\(\Rightarrow \frac{1}{2} Kx ^{2}=\frac{3 E }{4} \Rightarrow K =\frac{3 E }{2 x ^{2}}\)

\(\Rightarrow K =\frac{3 E }{2 \times\left(\frac{1}{4}\right)^{2}}=24\,E\)

\(n =24\)