Understanding how forms intersect
Before we actually get to the exercise itself, we're going to discuss how forms intersect - or more specifically, how we come up with the lines we draw to represent those intersections. People have inordinate amounts of trouble with this, and I don't expect you to be able to do this correctly right at lesson 2, but I do want you to give it a shot.
If I were to summarize how these intersections work, it would be this: Intersection lines sit exactly where they are able to run along the surfaces of both forms simultaneously.
To understand what this means, lets step back a little and look at this diagram depicting three kinds of intersections.
An intersection between two lines occurs at a point. This is a point in space that happens to sit on both lines simultaneously. The yellow point on the diagram sits only on the blue line, the purple point sits only on the green line, and the pink point sits on neither and is just floating arbitrarily in space. The red point however sits on both lines at the same time, and is therefore the intersection between them.
An intersection between two planes in 3D space occurs instead in a line - or more accurately, at any points that sit on both planes simultaneously. This also applies to any 2D shapes sitting in 3D space, even if those 2D shapes are bent or warped.
Finally, An intersection between two 3D forms can be represented by a 2D shape (that can be bent/deformed in space). The edges of this shape run along the surfaces of the two forms simultaneously. You'll never find an edge of this shape that exist only on the surface of one of the forms at a time.
This intersection shape can be quite difficult to figure out, and a big reason for this difficulty is that when we draw two forms in space, we decide where exactly they are. The intersections themselves allow us to describe these specific positions to others, but until we actually draw these intersections, how those forms relate to one another is not yet defined.
If you ignored the red intersection line in this diagram, you could argue that the blue box was floating completely in front of the cylinder, or behind it, or you could claim that they were intersecting in a different manner altogether. Once that red shape is drawn however (or more specifically the red line - the fainter red section is the part we wouldn't be able to see without x-ray vision), their relationship is cemented.
This is why form intersections are so critical, and why they become an extremely important tool for you - because it's your job to explain to your audience how the forms you've drawn relate to one another in the space you've created.