About finding the points that result. You can apply the transformations to the points as you go or you can find the intercepts and notable points after with a little algebra. e.g. for 4e. to find the x-intercepts you have
y=2-|x2-2|
x-intercepts, y=0
2-|x2-2|=0
|x2-2|=2
now the mod will make a negative value inside it positive and leave a positive value as positive.
i.e. x2-2=2 (when x2-2>0) and -(x2-2)=2 (when x2-2<0)
x2=4 or x2=0
x=+-2 or x=0
i.e. x-intercepts at (-2,0), (2,0) and (0,0)
Do the same for the y-intercept and use the transformations to find the turning point.
EDIT: e.g. original t.p at (0,-2)
Apply the mod, all the negative y-values will become positive as it is flipped in the x-axis.
(0,-2)->(0,2)
Then apply the whole reflection of the graph in the x-axis.
(0,2)->(0,-2)
Then apply the shift of two units up.
(0,-2)->(0,0)