If the solution of the differential equation \( (2x + 3y - 2)\,dx + (4x + 6y - 7)\,dy = 0 \), \( y(0) = 3 \), is \( \alpha x + \beta y + 3 \log_{e} |2x + 3y - \gamma| = 6 \), then \( \alpha + 2\beta + 3\gamma \) is equal to ____________.
