As you progress in the game, you'll eventually find the need to obtain dye and fabric -- mostly used as a part or ingredient to craft some higher tiered items to get past certain challenges later on in the game. To earn these stuff, you'll mostly be led to get them through the Store of Starlight -- using the special currency Starlight Coins. In this store, you'll have to buy dyes for 8 Starlight Coins and fabrics for 20. Take note though, that the only way to earn these special currency is by winning or at least taking part in the Stylist's Arena -- which when you think about it, would be tedious and costly as you are only rewarded 5 Starlight coins every time you win, and 3 when you lose (not to mention there is a limit to the number of times you could participate in a day).
Meanwhile, you can obtain dyes and fabrics in the Association Store as well (random) for 10 and 24 Association Coins respectively. Though you might think the value in terms of numbers are a bit higher, Association Coins are far easier to obtain than Starlight Coins.
Additional Tip:
You might want to hoard on those Starlight Coins you have for your recipes when crafting later on in the game.
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