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Add one to a hexagons number of vertices
A hexagonal prism has 12 vertices, 8 faces and 18 edges. A hexagonal pyramid has 7 vertices, 7 faces and 12 edges.
A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges. 7 vertices
To find the number of vertices on any pyramid, take the number of corners on the base and add 1 (for the top) A hexagonal based pyramid has 7 vertices (6 for the hexagon, 1 for the top) I suspect you might mean "hexagonal prism" though. In which case, for prisms, you double the number of corners in the 2D shape. A hexagonal prism has 12 vertices (6 for the hexagons at each end.)
An octahedron is the name for a non-specific shape. It could, as described above, be a di-rectangular pyramid with 6 vertices. Or it could be a heptagonal pyramid, in which case it has 8 vertices. Or it could be a hexagonal prism, in which case it has 12 vertices. There are other octahedraons.