Answer
$f(x)-2$: down 2 units
$f(x-2)$: right 2 units
Work Step by Step
The function $f(x)-2$ shifts the graph of $f(x)$ down 2 units, while the function $f(x-2)$ shifts the graph of $f(x)$ right 2 units. The first is a $y$ (vertical) transformation, while the second is an $x$ (horizontal) transformation.