Beginner here, so please someone else correct me if I'm wrong. One of the points that Uncomfortable makes about this exercise is that how the forms intersect is open to interpretation. You just want to be consistent for a believable look. When I look at the larger figures, the two planes closest appear to be flush, mostly, as drawn. If that is what you wanted, then the problem is not at the green line but the other face closest to the viewer. The dark line should be just like the other side and all the way back instead of having a "cut out section". The planes seem to share the same vanishing point which is why they appear flush to me. If you want them to skew a little, they should have different vanishing points. (Again, if I have said something incorrect please let me know. I am learning too).

Firstly, this is not easy. You are training your brain to be able to imagine how things interact in 3d space.

The objects can be interpreted in different ways but mainly in which object is in front of another and this will dictate which object is being cut into and which is doing the cutting.

In the case of your second one it seems like the larger box could be engulfing the smaller one. When starting it would be best to start with objects which don't overlap as much as these ones day. i have linked my very rough interpretation of the forms here.

https://imgur.com/a/KuxJt9H

In general when I did this lesson. I tended to follow an edge into the other object and stop when the edge intersected the plane it was approaching. This requires visualisation to decide if it is convincing. I would then try and imagine the edge created by the planes intersecting and follow that. Continue until the whole intersection is outlined.

Scoobyclub's picture is very helpful and explains things better than I did (imagine that, a picture is worth a bunch of words).

When I first did this assignment, I did something that I am not sure Uncomfortable would agree with but it helped me alot. For practice, I drew the intersecting shapes just as assigned, drawing through them so that all lines were visible. I then took some whiteout and covered up the lines that would not be visible as if you couldn't see through the boxes. That gave me a view similar to what Scoobyclub showed. If I made a mistake, it usually became a glaring one when I did that. I only had to do that on one practice page before I was able to see the intersections better. Again, I don't know if Uncomfortable would agree, but it helped me personally.