In a \( \triangle ABC \), suppose \( y = x \) is the equation of the bisector of the angle \( B \) and the equation of the side \( AC \) is \( 2x - y = 2 \). If \( 2AB = BC \) and the points \( A \) and \( B \) are respectively \( (4, 6) \) and \( (\alpha, \beta) \), then \( \alpha + 2\beta \) is equal to:
