Hi there - just add a Geodatabase Reader (ArcObjects if you have ESRI installed and API reader if not). Then browse to multiple GDB files at once like this:

...or go for c:\\temp\\**\\*.gdb or similar. Then make sure 'Single Merged Feature Type' is tagged.

Then add an AttributeExposer to your feature type and expose fme_basename (for the filename) and fme_feature_type (for the featureclass name) so that you know what came from where. You'll then be able to conflate the content to a single target GDB with a GDB writer.

Something like this perhaps. filegdb2filegdb.fmw

DO you want to merge the feature classes into one new feature class?

Or do you want to add all feature classes into one new file geodatabase?

David answered the first option.

If the second is what you need:

Use the reader as David suggested but do not merge feature types, just use individual feature types.

Add a Writer to a new File geodatabase and use the option to copy from reader.

This will make a copy of all tables into a new file geodatabase.