Two immiscible liquids of refractive indices (8)/(5) and (3)/(2)...

The formula to calculate the apparent height of the coin when seen through the combination of liquids can be written as

${h}_{app} = \dfrac{{h}_{1}}{{\mu}_{1}} + \dfrac{{h}_{2}}{{\mu}_{2}} . . . \left(1\right)$

From equation (1), it follows that

$\begin{cases}{h}_{app} & = & \dfrac{6}{3 / 2} + \dfrac{6}{8 / 5}cm \\ & = & 4 + \dfrac{15}{4}cm \\ & = & \dfrac{31}{4}cm\end{cases}$

Hence, $\alpha = 31$.