Let α β γ=45; α, β, γ ∈ R. If x(α, 1,2)+y(1, β, 2)+z(2,3, γ)=(0,0,0) for some x, y, z ∈ R, x y z ≠ 0, then 6 α+4 β+γ is equal to ____

Let $\displaystyle \alpha \beta \gamma=45 ; \alpha, \beta, \gamma \in \mathbb{R}$. If $\displaystyle x(\alpha, 1,2)+y(1, \beta, 2)+z(2,3, \gamma)=(0,0,0)$ for some $\displaystyle x, y, z \in \mathbb{R}, x y z \neq 0$, then $\displaystyle 6 \alpha+4 \beta+\gamma$ is equal to $\displaystyle \_\_\_\_$