After Marion adds 6 to both sides of the equation \(9x - 6 = 12\), the equation becomes:
\[ 9x - 6 + 6 = 12 + 6 \]
This simplifies to:
\[ 9x = 18 \]
In the next step, to solve for \(x\), she needs to divide both sides by 9. So, the value that each side needs to be divided by is:
\[ \text{Divide by } 9. \]