The solubility of AgSCN in pure water is x times its solubility in...

Let the solubility of $\text{AgSCN}$ in pure water be $s_1$.

For pure water:
$\text{AgSCN}(s) \rightleftharpoons \text{Ag}^+(aq) + \text{SCN}^-(aq)$
$K_{sp} = s_1^2$
$s_1 = \sqrt{10^{-12}} = 10^{-6}\text{ M}$

Let the solubility of $\text{AgSCN}$ in $0.001\text{ M KSCN}$ be $s_2$.
Due to the common ion effect, $[\text{SCN}^-] = s_2 + 0.001 \approx 10^{-3}\text{ M}$ (since $s_2$ is very small compared to $10^{-3}$).
$K_{sp} = [\text{Ag}^+][\text{SCN}^-] = s_2 \times 10^{-3}$
$s_2 = \dfrac{10^{-12}}{10^{-3}} = 10^{-9}\text{ M}$

Given that $s_1 = x \times s_2$
$x = \dfrac{s_1}{s_2} = \dfrac{10^{-6}}{10^{-9}} = 10^3$

Answer: $10^3$