Which of the following order is correct for strength and extent of H-bonding between ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{H}}_2{\mathrm{O}}_2$ respectively:

The strength of H-bonding is greater in ${\mathrm{H}}_2\mathrm{O}$ than in ${\mathrm{H}}_2{{\mathrm{O}}_2}_{ }$ because water has more formal negative charge on the oxygen atom than ${\mathrm{H}}_2{\mathrm{O}}_2$.
Because of the largest electronegativity difference between H and F, HF has the strongest hydrogen bond. The hydrogen molecule is covalently bonded and does not exhibit hydrogen bonding.
As a result, the order is $\mathrm{HF}>{\mathrm{H}}_2\mathrm{O}>{\mathrm{H}}_2{\mathrm{O}}_2>{\mathrm{H}}_2$.