As shown in the figure, three identical metal plates having large...

Let the charges on the three plates from left to right be $Q_1 = Q$, $Q_2 = 0$, and $Q_3 = -2Q$.

The total charge on the system of plates is:
$Q_{\text{total}} = Q_1 + Q_2 + Q_3 = Q + 0 - 2Q = -Q$

For a system of parallel conducting plates, the charge appearing on the outermost surfaces of the leftmost and rightmost plates is always equal and is exactly half of the total charge of the system. This is a direct consequence of Gauss's law and the fact that the electric field inside the bulk of the conducting plates must be zero.

Let $q_{\text{outer}}$ be the charge on the outer surface of the rightmost plate. Then:
$q_{\text{outer}} = \dfrac{Q_{\text{total}}}{2} = \dfrac{-Q}{2}$

Thus, the charge that appears on the outer surface of the rightmost plate is $-Q/2$.