Number of effective Y atoms = (8 corners X 1/8 per corner atom share +6 faces X $\frac{1}{2}$ per middle of the atom share) 

                                               =( 8 X 1/8 +6 X $\frac{1}{2}$) 

                                               = 4 

One Y atoms create 2 Y tetrahedral voids = 2 X 4=8

Number of effective X atoms =$\frac{1}{3}$x 8 =$\frac{8}{3}$X

Formula of unit cell = ${\mathrm{X}}_{\frac{8}{3}}{\mathrm{Y}}_4 ={\mathrm{X}}_2{\mathrm{Y}}_3$