\(n =\) initial frequency

\(\omega=2 \pi n\)

Initial kinetic energy is

\(K _{ i }=\frac{1}{2} I \omega^2=\frac{1}{2} I \times 2 \pi n \times 2 \pi n\)

\(K _{ i }=2 I \pi^2 n ^2\)

When frequency is double to the initial frequency, the the kinetic energy will be

\(K _{ f }=\frac{1}{2} I \omega^2=\frac{1}{2} I \times 4 \pi n \times 4 \pi n\)

\(K _{ f }=8 I \pi^2 n ^2\)

By work-energy theorem,

\(W = K _{ f }- K _{ i }\)

\(W =8 I \pi^2 n ^2-2 I \pi^2 n ^2=6 I \pi^2 n ^2\)