Marion's equation is \( 9x - 6 = 12 \). After adding 6 to both sides, the equation becomes:
\[ 9x - 6 + 6 = 12 + 6 \]
This simplifies to:
\[ 9x = 18 \]
Now, to isolate \( x \), Marion needs to divide both sides of the equation by the coefficient of \( x \), which is 9. Therefore, each side needs to be divided by:
\[ 9 \]
So, the value by which each side should be divided is 9.