The function $h$ is defined by $h(x)=4x+28$. The graph of $y=h(x)$ has an $x$-intercept at $(a,0)$ and a $y$-intercept at $(0,b)$. A new function $g$ is defined by $g(x)=h(x)-12$. If the graph of $y=g(x)$ has an $x$-intercept at $(c,0)$ and a $y$-intercept at $(0,d)$, what is the value of $c+d$?