In fcc unit cell, two tetrahedral voids are formed on each of the four non-parallel body diagonals of the cube at a distance of 3​a/4 from every corner along the body diagonal.
The angle between body diagonal and an edge is cos−1(1/3​). So, the projection of the line on an edge is a/4.
Similarly, other tetrahedral void also will be a/4 away.
So, the distance between these two is [a−4a​]−4a​=2a​.