You can get Synthesis Image Support from two NPCs in your Guild.
One of the NPCs will boost your skill by one level for a period of a few minutes for free. The other one will boost your skill by two levels for a period of a little over eight minutes for a fee. This fee increases alongside your rank.
To get the support, just talk to the NPC and accept the Synthesis Image Suppert they offer.
See the Guild you want support from to find the NPC that gives it: Crafts