Marion starts with the equation:
\[ 9x - 6 = 12. \]
After adding 6 to both sides, the equation becomes:
\[ 9x - 6 + 6 = 12 + 6, \]
which simplifies to:
\[ 9x = 18. \]
In the next step, to isolate \( x \), she needs to divide both sides by 9. Therefore, each side needs to be divided by:
\[ 9. \]