To solve this problem, we need to use Euler's formula for polyhedra, which relates the number of faces (F), edges (E), and vertices (V) of a polyhedron. Euler's formula states: V−E+F=2 Calculation: 1. Given values: Faces (F)=7, Edges (E)=15, and Vertices (V)=x. 2. Substitute the given values into Euler's formula: x−15+7=2 x−8=2 x=10 3. Now that we know the value of x (vertices) is 10 , we can calculate the value of the expression ( 2F+3E−4x ): 2F+3E−4x=2(7)+3(15)−4(10) =14+45−40 =19