The graph of a linear function $g(x)$ passes through the points $(0,8)$ and $(4,0)$. The graph of another linear function $h(x)$ passes through the points $(0,2)$ and $(6,0)$. If $k$ is the $x$-intercept of $g(x)$ and $m$ is the $y$-intercept of $h(x)$, what is the value of $k+m$?