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Two options:
1) Backup / Restore
On computer B, open rekordbox, go to File > Library > Backup Library, create a backup zip file of the database and (optionally) all your music files as well (you are prompted if you want to copy them). You may want to do this to an external USB drive to not take up space on your internal drive, and for ease of moving it to the other computer. On computer A, open rekordbox, go to File > Library > Restore Library and select the backup file. It will warn you that you're about to overwrite the database on that computer, you can allow it and then you'll have a copy of the library and all music (if copied) on computer A as well.
2) External Database / Music
See this article and video for instructions on moving your database and music to an external drive for use with multiple computers.