Starting with your form intersections, I think there is some advice I can offer on how to think through these spatial relationships that should help. Of course, this exercise is still quite challenging, but you should be at a point in your development (given the fact that you've been playing around with combining many different kinds of forms together in 3D space in Lessons 3-5) that this advice may help in a meaningful way.

If you take a look at this page, I've both drawn some corrections on top of your existing work, and have also marked out some arrows denoting the curvature of different surfaces in specific directions. These arrows can be thought of as the building blocks of our eventual intersection lines.

For example, if we look at the sphere-cone intersection in the bottom left, we've got three arrows drawn here. One curve following the rounded section of the cone, then one following the curvature of the sphere (specifically the slice of that sphere that would run parallel with the cone's own length, defined by its minor axis), and then another following the cone's curve once again. The actual resulting intersection, though it's not the clearest it could be, is a sort of S curve where it transitions from that first of the cone's arrows, into the sphere's arrow - then if we could see the other side beyond the sphere, we'd see it curve back to follow the cone.

We can see a similar deal with the cylinder-sphere intersection on the right side of the page, where it goes from following the cylinder, to the sphere, and back to the cylinder. These arrows are the pieces we fit together to find how this intersection line is going to continue to sit along the surface of both forms simultaneously, and at all times.

Conversely if we look at how you approached this sphere-box intersection with a single, unbroken curve that follows the surface of the sphere, we actually find that it cannot possibly be following the surfaces of the box at the same time. Rather, that intersection line passes through the volume of the box - it must, since it's a single continuous curve in 3D space, following that sphere's surface. As soon as we hit the edge of the box, its faces change dramatically, rotating 90 degrees - that can't be achieved with a single continuous curve. And so, as you can see the same intersection in my markup of the page, we actually have two distinct curves, which meet at the box's edge.

I didn't draw the arrows in for this one, but in effect, we're looking at two slices of the box, each one parallel with one of the cube's faces. That way we can ensure that each individual curve is going to run along the box's face as well as the sphere's surface, and those two meet at the box's edge.

With that out of the way, let's take a look at your object constructions. By and large here you've done a pretty great job. I have just a couple of points to offer suggestions/corrections on, but as a whole I'm very pleased to see that you've on various levels shown a good deal of respect for the emphasis this lesson has on precision. Precision is often conflated with accuracy, but they're actually two different things (at least insofar as I use the terms here). Where accuracy speaks to how close you were to executing the mark you intended to, precision actually has nothing to do with putting the mark down on the page. It's about the steps you take beforehand to declare those intentions.

So for example, if we look at the ghosting method, when going through the planning phase of a straight line, we can place a start/end point down. This increases the precision of our drawing, by declaring what we intend to do. From there the mark may miss those points, or it may nail them, it may overshoot, or whatever else - but prior to any of that, we have declared our intent, explaining our thought process, and in so doing, ensuring that we ourselves are acting on that clearly defined intent, rather than just putting marks down and then figuring things out as we go. In our constructions here, we build up precision primarily through the use of the subdivisions. These allow us to meaningfully study the proportions of our intended object in two dimensions with an orthographic study, then apply those same proportions to the object in three dimensions.

Given how we've essentially come out of a number of lessons that don't put the same kind of emphasis on this principle (they were vastly more forgiving - we'd often eyeball the intended size of our forms without declaring it ahead of time, and then keep rolling ahead with whatever result we had), it is not uncommon for students to feel less inclined to push their precision as far as it can reasonably go. For the most part, I think you've done quite well with this - although there can be some improvement.

One construction that caught my eye was this lava lamp - specifically because the individual points at which you'd established cross-sectional slices to gradually build out the form itself seemed to be pretty approximate. What would be better in this regard is to first start with an "orthographic" study - that is, a side view of the object, where you can enclose it into a rectangle and then identify where along that rectangle's length each cross-section should fall.

Such an orthographic study might look like this, where we use subdivision to give ourselves an idea of specifically where each landmark should fall. This doesn't have to be perfect, but having such a plan laid out can help take the burden off us later when we try to make these decisions in 3D space. With this already laid out, we simply have to recreate the grid in 3D space (using the techniques from the lesson notes).

Continuing on, looking at your pill bottle, if we actually extend out the lines for that box as shown here, we can pretty quickly find that they're rather wonky. Given that you do have the freedom to use a ruler here (and I assume you are), you can ostensibly see where those lines would extend to prior to drawing them - so simply taking a bit more time to use your tools more effectively will help you avoid these kinds of issues.

The last thing I wanted to call out is that the cast shadow shapes you outline (the ones for the overall object) tend to look out of place, so I extended out some lines to try and understand what you were going after. As shown here, if we extend out that cut-off edge from your shadow shape, it doesn't actually connect to the base of the object, which it definitely should. I'm not really sure how you're thinking through those shadow shapes, but right now yours are not actually sitting on the surface of the ground plane at all, so you'll want to consider that going forward.

Anyway, all in all you're moving in the right direction, and are holding to the core principles of the lesson well, though you do have a number of things to keep in mind. I'll go ahead and mark this lesson as complete.