We are given an octagonal prism and we are asked to determine the number of faces and the number of vertices. Since the base of an octagonal prism is an octagon this means that the base has 8 sides, each side represents a face in the prims, therefore we have 8 faces plus 2 faces of the bases for a total of 10 faces.
For the number of vertices, we have that each base has 8 vertices because it is an octagon, therefore, there must be 16 vertices (8 for each base). Therefore, we have 10 faces and 16 vertices.