To solve the equation \( \frac{y}{2} = \frac{4}{20} \), start by simplifying the fraction on the right side.
\[ \frac{4}{20} = \frac{1}{5} \]
Now the equation becomes:
\[ \frac{y}{2} = \frac{1}{5} \]
Next, to eliminate the fraction, multiply both sides of the equation by 2:
\[ y = 2 \cdot \frac{1}{5} \]
This simplifies to:
\[ y = \frac{2}{5} \]
So, the solution is:
\[ \boxed{\frac{2}{5}} \]