we know that
The diameter of circle B is 8 inches
so
BX=8/2=4 inches ------> The radius is half the diameter
The diameter of circle A is 10 inches
so
AY=10/2=5 inches ----> The radius is half the diameter
XY=AY-AX
XY=5-3=2 inches
therefore
BX=XY+YB ----> by addition segments postulate
substitute given values
4=2+YB
solve for YB
YB=2 inches