To solve the equation
\[ \frac{13 - y}{17 - y} = 2, \]
we can start by cross-multiplying to eliminate the fraction:
\[ 13 - y = 2(17 - y). \]
Expanding the right side:
\[ 13 - y = 34 - 2y. \]
Next, we'll isolate \( y \) by adding \( 2y \) to both sides and also subtracting 13 from both sides:
\[ -y + 2y = 34 - 13, \]
which simplifies to:
\[ y = 21. \]
So the solution to the equation is
\[ y = 21. \]