One definition of gram-equivalent is the mass of a substance that will combine with 1.008 g of hydrogen.
If we are talking about molecules of oxygen,
#color(white)(ll)2"H"_2color(white)(m) +color(white)(m) "O"_2color(white)(m) → 2"H"_2"O"#
#"4.032 g"color(white)(mm)"32.00 g"#
If we are talking about atoms of oxygen,
#color(white)(m)"H"_2 color(white)(m)+color(white)(m) "O"color(white)(m) → "H"_2"O"#
#"2.016 g"color(white)(ml)"16.00 g"#
In either case, 1.008 g of hydrogen combines with 8.000 g of oxygen.
∴ One gram-equivalent of oxygen has a mass of 8.000 g.
#"Number of O atoms" = 8.000 color(red)(cancel(color(black)("g O"))) × (1 color(red)(cancel(color(black)("mol O"))))/(16.00 color(red)(cancel(color(black)("g O")))) × (N_text(A)color(white)(l) "O atoms")/(1 color(red)(cancel(color(black)("mol O")))) = N_text(A)/2color(white)(l) "O atoms"#.
