You’ll have to attach Database X with Database Y using the ATTACH command, then run the appropriate Insert Into commands for the tables you want to transfer.
INSERT INTO X.TABLE SELECT * FROM Y.TABLE;
// "INSERT or IGNORE" if you want to ignore duplicates with same unique constraint
Or, if the columns are not matched up in order:
INSERT INTO X.TABLE(fieldname1, fieldname2) SELECT fieldname1, fieldname2 FROM Y.TABLE;