For an amplitude modulated wave the minimum amplitude is 3V , while...

Modulatio index is the ratio of the difference in amplitudes to the sum of the amplitudes.

The formula to calculate the modulation index of a wave is given by

\mu = \dfrac{{A}_\max - {A}_\min}{{A}_\max + {A}_\min} . . . \left(1\right)

Substitute the values of the known parameters into equation (1) and solve to calculate the required value of maximum amplitude.

\begin{cases}0 . 6 & = & \dfrac{{A}_\max - 3}{{A}_\max + 3} \\ & ⇒ & 0 . 6{A}_\max + 1 . 8 = {A}_\max - 3 \\ & ⇒ & 0 . 4{A}_\max = 4 . 8 \\ & ⇒ & {A}_\max = \dfrac{4 . 8}{0 . 4} \\ & = & 12V\end{cases}