When the figure above is cut along the solid lines, folded along the

You can ignore the diagram completely (as I did when I solved it) because the question tells you that you get a figure with "2 pyramids each with a square base that they share". Imagine what one pyramid looks like - a square with triangles attached to each side and the tips of the triangles stuck together. Imagine how would you have two pyramids with a common base. There would be 4 triangles on the lower side of the square too and their tips would be stuck together. So in all, the figure would have 8 faces (4 triangles + 4 triangles) and 12 edges ( 4 edges where the top triangles join, 4 edges where the bottom triangles join and 4 edges of the square).
All in all you will have 8 + 12 = 20 faces + edges

i'm having a hard time seeing how folding makes an Octahedron - i wonder if there is a video illustrating this

The moment the octa hedron is drawn, the edges of the square as well as the square bases of two pyramids merge and should ideally be considered as one. so it should be only 6 edges (4 for square and two pyramid tips) + 8 face = 14. Honestly it seems like a flawed question here.