Step 1: Recall the rule.
The perpendicular distance of a point \( (x, y) \) from the \(y\)-axis is \( |x| \). Step 2: Substitute the coordinates.
For \( (13, 15) \), distance from the \(y\)-axis \(= |13| = 13 \). Step 3: Conclude.
Hence, the required distance is \( 13 \).