Answer
$-3.0\times 10^{-6}~C$
Work Step by Step
The net electric field within the metal must be zero. Therefore, the enclosed charge within the shell (including the inner surface of the cavity wall) must be zero. That is, the sum of the charge on the inner surface and the charge of the particle must be zero.
We can find the charge $Q$ on the cavity wall:
$(+3.0\times 10^{-6}~C)+Q = 0$
$Q = -3.0\times 10^{-6}~C$
