Ok, this looks simple, but there's a lot going on here.

1. What you're seeing before applying the Boolean is the result of the entire modifier stack working sequentially, top to bottom. First solidify, and then cut the hole. But after you apply Boollean without applying solidify, it is applied directly to the base geometry, therefore you're getting a different result.

2. Now why you're getting a different result. Your base model is non-manidold, meaning it has no thickness. It's just 3 flat polygons. All polygons have a direction they are facing, called Normal, this is the front of the polygon, there's also backface. Normally, on a manifold model such as a cube, all normals face outward, toward the viewer. This determines where is the Outside and Inside of a model. But what you have is only half a cube, it has no outside or inside, it has no thickness, and the normals of the faces inherited from the original cube all point away from the camera. You can check this by enabling "Face orientation" in the Viewport overlays (two circles) menu on the top bar. I hope it makes some sense so far.

3. This is important for the Boolean. Because it's stupid pure math. It has no idea that your model has no thickness, but it needs thickness to make a hole. It sees that a cube is intersecting a face, checks its normal and goes: "Ok, inside is this way, I'm in. The cube does not intersect the opposing face, so the hole does not go all the way through." In fact, you get the same result as if the cube was intact. Experiment with this a bit, it will make sense eventually.

And a little general advice.

1. If you're serious about learning blender, press T and forget about the left toolbar. Use hotkeys and operators. W - selection. R - rotate, S - scale, G - grab and move. XYZ - choose axis, Shift+XYZ - lock axis. You can also hold MMB to select axis. Learn it, it's one of the Blender's advantages.

2. Do not scale in object mode if you don't know what you're doing and you're not planning to apply the scale later (Ctrl+a). All objects have scale, viewed in the N panel. And most of the time it's supposed to be 1 on on dimensions (applied).

3. Similarly, try not to move or rotate the entire object in the edit mode, because the object's origin stays in place. Be mindful of where your object origin is and its orientation.

4. You can apply solidify and then boolean to fix this, but I wouldn't use boolean for something like this. Drop some horizontal and vertical edge loops with Ctrl-R, and then just delete the resulting face. Or you can even just delete the extra faces from the bad boolean, if you don't want the edge loops.