If a solid shape has 6 faces and 12 edges, how many vertices the solid must have?

Euler's formula for polyhedrons gives the relation between the number of faces, edges and vertices in a solid. It is given as:

F + V - E = 2

Where F - faces, E - edges, and V - vertices.

From the given data,  F=6 and E=12

$\Rightarrow$6 + V - 12 = 2

$\Rightarrow$V - 6 = 2

$\Rightarrow$V = 2 +6

$\Rightarrow$V=8

Therefore, if a solid shape has 6 faces and 12 edges then it must have 8 vertices.