How Many More Vertices Does A Triangular Prism Have Than A Triangular Pyramid?

First step - draw a diagram of the two shapes you are comparing.

A trangular pyramid has a triangular base with three triangles joining at a top vertex.

so it has 4 vertices in total.

A triangular prism has a triangle at each base, joined with paralell lines (between which, rectangular shapes are created)

so each triangle creates 3 vertices, so a triangular prism has six vertices in total.

the prism has 2 more vertices than a triangular pyramid.

I hope this helps.