For an amplitude modulated wave the minimum amplitude is $3 \mathrm{V}$, while the modulation index is $60\%$. The maximum amplitude of the modulated wave is:

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

$\mu =\frac{A_{\max }-A_{\min }}{A_{\max }+A_{\min }} ...\left(1\right)$

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

$\begin{array}{rcl}0.6& =& \frac{A_{\max }-3}{A_{\max }+3}\\ & \Rightarrow & 0.6A_{\max }+1.8=A_{\max }-3\\ & \Rightarrow & 0.4A_{\max }=4.8\\ & \Rightarrow & A_{\max }= \frac{4.8}{0.4}\\ & =& 12 \mathrm{V}\end{array}$