If x and y vary inversely and x = 15 when y = 6,

$x$ and $y$ var $y$ inversely.

i.e. $x y=$ constant

Now, $15 \times 6=9 \times y_{1}$

$\Rightarrow y_{1}=\frac{15 \times 6}{9}$

$\Rightarrow y_{1}=10$

$\therefore$ Value of $y=10$, when $x=9$