Garuda HM quest cannot be found.

Thread name: Garuda HM　quest cannot be found.
Time: Yesterday
Frequency: Always
World name: Cactuar
Character name: Regna Farron
NPC name: N/A
Monster name: Garuda
Class/level: Paladin/50
Party or solo:
Race: Hyur Male

After I beat the Ifrit, quest got updated and ask me to obtain howling gale from Howling Eye (HARD). However, I went to the place and found myself unable to attune the crystal, theres no quest mark whatsoever. Garuda hard is not on my duty list. On the quest log, it still tells me to get white-hot ember from ifrit eventho I have beat him multiple time.

I did beat Ifrit once before the quest even asked me to long time ago as a Warrior,
now the quest I'm doing is for Paladin's ultimate weapon.

To unlock Garuda HM, you need to go to the Waking Sands to get the quest "In for Garuda Awakening." Complete that quest and you should have access to The Howling Eye (Hard) in the Duty Finder.