Count the discrete databases the library subscribes to under the larger publisher umbrella.   For instance, under the state database licensing agreement, there are 26 licensed EBSCOhost databases.  Ebsco merges some databases, adds another, etc., but by contract there are always 26.   In the EBSCOhost family of databases, a library may choose to subscribe to an auto repair database by itself.  This would make 27 EBSCOhost databases.

If, however, one buys a block of generic searches usable across an array of databases in a family (ala OCLC), count that as one database.