Dye armor

[Rongway]

[general dye info]

I think they're specifically asking about the job-specific artifact gear.

The ARR AF1 gear (Lv45/50) comes in three versions: the IL50/55 gear, the IL90 AF1+ recolor, and a third version that is dyable. You have to have an Alchemist craft the appropriate augmentation kit and then take that along with the original gear to Rowena's castle in Mor Dhona to trade for the dyable version.

The HW AF2 gear should be dyable as soon as you get it from the vendor since they only sell the upgraded dyable version now.

SB AF3 requires doing Eureka.

ShB AF4 requires doing a certain trial extreme (the one that doesn't drop a mount):

Memoria Miseria

EW AF5 requires completing the related role quest line.