Answer
Shift $4$ units downwards.
Work Step by Step
The graph of
$$
g(x)=x^2-4
$$ is similar to the graph of the parent function, $f(x)=x^2$, which is a parabola that opens up and has a vertex at $(0,0)$. The graph of $g(x)$, though, has all the points of the parent function shifted $4$ units downwards.
