Direct migration from previous Search versions is not possible. You can export the following from your Search 2006.x installation as XML files, and then import it into your Search 9.3 installation:
Dictionaries
Term Weight Sets
Taxonomies (called Topic Sets in Search 9)
Note: Be sure to export topic sets from 2006.x so that the topic IDs are included, and import them into Search 9 the same way. If you do not include topic IDs, topic references are broken.
Query Rules
Document Parsing Options (called Text Processing Option Sets in Search 9)
Refinement Configurations (called Facet Sets in Search 9)
Warning: All data must be exported using the 2006.x Management Console. Make sure to export your data before uninstalling Search 2006.x.