The $\mathrm{pH}$ of solution is 9 . It is times more basic than a solution with $\mathrm{pH}=6$.

It is given to find how much times more basic than a solution with $\mathrm{pH}$=6, if $\mathrm{pH}$ of solution is 9.

$\mathrm{pH}=-\log \left({\mathrm{H}}^{+}\right)$

$9=-\log \left({\mathrm{H}}^{+}\right)$

${10}^{-9}={\mathrm{H}}^{+}$

we need to find less basic solution,i.e. more acidic so more ${\mathrm{H}}^{+}$concentration in the new solution.

So

${\mathrm{H}}^{+}\text{ in new solution }={10}^{-9}x1000={10}^{-6}$

$\mathrm{pH}\text{ of new solution }=-\log \left({10}^{-6})\right)=6$

so $\mathrm{pH}$ =9 is 1000 times more basic than $\mathrm{pH}=6.$

Hence the correct answer (C) 1000