Question

A cell centered cubic bases containing 8 X atoms at the vertices of the cell and Y 6 atoms cheeks. What is the empirical formula of the solid?

Answer 1

Obviously, you meant the face-centered cubic lattice, not cell-centered.
In the face-centered cubic lattice, only 1/8 of each atom on the vertex lies within the cell. And 1/2 of each facial atom lies within the cell.
Let's calculate the formula of the compound from the given data:
X_nY_m
n = 8*1/8 = 1
m = 6*1/2 = 3
So, we have a compound of formula XY₃, which is crystallized in the face-centered lattice. An example of such compound is the potassium nitride K₃N.