I really need help *there is a picture*

Wow, that looks like a lot of work.  Let's see what I can do on the figure.

Key ideas:

Translation, we just add the indicated values to x and y

Rotation CCW 90 (x,y) to (-y,x)

Rotation CW 90  (x,y)  to (y,-x)

Reflection in x axis: (x,y) to (x,-y)

Reflection in y axis: (x,y) to (-x,y)

Rotation by 180: (x,y) to (-x,-y)

There was one that I didn't think had any path (and others if you look at the boxes that you don't get to) but I plowed through.