Can someone explain this?

[Hunus]

How does one use ratios of gas densities to estimate the molecular mass and find the molecular
formulas?

[MrSid]

Conceptually keep in mind Ideal Gas Law PV=nRT can allow one to show that at STP one mole of gas molecules exist in 22.4 liters of volume.
since gas density is gms/ liter (mass/volume) one can calculate the gms of gas from the density to make 22.4 liters or one mole of gas.... gms per mole then gives a Gram Molecular Weight

If the density is given at a different temperature and pressure recalculate it for STP

[Borek]

Conceptually keep in mind Ideal Gas Law PV=nRT can allow one to show that at STP one mole of gas molecules exist in 22.4 liters of volume.
since gas density is gms/ liter (mass/volume) one can calculate the gms of gas from the density to make 22.4 liters or one mole of gas.... gms per mole then gives a Gram Molecular Weight

You are right, but mixing mass and "grams of gas" in one sentence is not a good idea. "Grams" are not a synonym of "mass".

If the density is given at a different temperature and pressure recalculate it for STP

No need for that - you can calculate volume of 1 mole of gas for these conditions and use this volume to calculate mass of 1 mole.