Total length= length covered by red beads + length covered by blue beads + length covered by white beads
16 inches = 4 1/4 inches + 8 3/8 inches + x
16 inches = 17/4 + 67/8 + x
16 inches = (34+67)/8+ x
16 inches = 101/8 + x
x= 16 - 12 5/8 inches
x= 3 3/8 inches.
3 3/8 inches are filled with white beads.