Question

Graph y= |x| -2
graph y=-|x-4|

Answer 1

y=|x| -2 moves up 2.

y=-|x-4| you move up 4 as well.

Answer 2

The graph y = |x| - 2 would move the V shape down 2 units from the vertex.
The graph y = |x - 4| would move the V shape to the right 4 units from the vertex.
Hope this helps!!!