The intersecting chords theorem states that whenever two chords intersect, the product of their pieces is constant.
So, in this case, we have
[tex]\overline{RW}\cdot\overline{WP}=\overline{SW}\cdot\overline{WQ}[/tex]
Plugging your values, we have
[tex]8\cdot 9 = 6x \cdot 12x \iff 72=72x^2 \iff x^2=1[/tex]
This equation has solutions [tex]x=\pm 1[/tex], but we can't choose [tex]x=-1[/tex], because it would lead to
[tex]\overline{SW}=-6,\quad\overline{WQ}=-12[/tex]
So, the only feasible solutions is [tex]x=1[/tex]
