If x, y and z are respectively the number of faces, vertices and edges of a triangular pyramid, then :

The correct option is 2x+ 3y−2z=8.

Let us first determine the number of faces, vertices, and edges of a triangular pyramid (also known as a tetrahedron):

1. Number of faces (x): A triangular pyramid has 1 triangular base and 3 triangular sides that meet at the top apex.
Therefore, $x=4$.

2. Number of vertices (y): It has 3 vertices at the base and 1 vertex at the apex.
Therefore, $y=4$.

3. Number of edges (z): It has 3 edges connecting the base vertices and 3 edges connecting the base vertices to the top apex.
Therefore, $z=6$.

Now, let us evaluate the given options using the values $x=4$, $y=4$, and $z=6$:

For the option 2x + 3y − 2z = 8:

$\text{LHS}=2\left(4\right)+3\left(4\right)-2\left(6\right)$

$\text{LHS}=8+12-12=8$

$\text{LHS}=\text{RHS}$

Thus, the relationship $2x+3y-2z=8$ holds true.