Answer
White has 4 and gray has 8.
Work Step by Step
From the text:
White/$\beta$: $8\times1/8$ in the corners, $4\times1/2$ in the faces and one in the center: 4 total
Gray/$\alpha$: $8\times1/8$ in the corners, $6\times1/2$ in the faces and four in the center: 8 total
