Starting with the equation:
\[ 5y = 20x + 8 \]
After subtracting 8 from both sides, the equation becomes:
\[ 5y - 8 = 20x \]
To rewrite the equation in terms of \( x \), Tilda needs to isolate \( x \) on one side.
To do this, she can divide both sides of the equation by 20. So, the number she should divide both sides by is:
\[ 20 \]
Therefore, the answer is 20.