The position of an object moving along $X$-axis is given by $x=\alpha+\beta t^2$, where $\alpha$ and $\beta$ are constants with appropriate dimensions and $t$ is time in seconds. The average velocity between $t=2 \mathrm{~s}$ and $4 \mathrm{~s}$ is $12 \mathrm{~m} / \mathrm{s}$. If $\alpha=8 \mathrm{~m}$, then the value of $\beta$ is