There are mainly the following types of recipes and blueprints available in this game:
- Recipes for items crafted through Synthesis
- Recipes for exploration items crafted through Simple Synthesis
- Blueprints for objects (furniture) crafted through Building
If the recipe you obtained does not appear on the Synthesis screen, it might be a recipe for Simple Synthesis rather than for Synthesis or Building.
Please check the other screens to see if you can find the recipe there.