The number f-electrons in +3 oxidation state of gadolinium (Z= 64) is x and in +2 oxidation state of Ytterbium ( Z=70) is y. The sum of x and y is

Electronic configuration of Gd(Z=64) is [Xe]4f⁷5d¹6s². When Gd is in +3 oxidation state, then the number of f electrons becomes 7 (x = 7).

Electronic configuration of Ytterbium (Z=70) is [Xe]4f¹⁴6s². When Ytterbium is in +2 oxidation state, then the number of f electrons becomes 14 (y = 14).

x+y = 7+14 = 21