If there is an easier way of manipulating data I would appreciate suggestion.
That's the key question here as your current design would require making a very large number of relationships to your activities table, one for each option field.
Instead, look up "Portals" in FileMaker help. You should define a table, Registered_Activities, separate from Registrants to be used for logging each planned activity. A record in Registered activities would log a single activity for a specified registrant and time so you would only have one field in this record to link to the activities table in order to display the activity name.
Registrants---<Registered_Activities>----Activities (---< means one to many)
Based on this, unfortunately, separating data into another table is not an option.
What about a suggestion on calculation?
Logically it should be
Registrants::Day1_AM_op1_name = Activities::opt_ + "Registrants::Day1_AM_opt1" from record where Activities:act_name = Registrants::Day1_AM_act_name
I don't think you have a reasonable option but to add a related table. There are ways to script the transfer of data from your current file into the related table.
Your calculation field will hit the same limitation as far as I can see.
If I've analyzed your original post accurately, you have 20 options per day for 6 days ( the 6 tabs that I see). That's 120 different options fields, and that in turn requires 120 different relationships, one for each option field. See how ugly that's going to be?
I suppose you could script a lookup, but this will be far from the best approach for implementing this. Both the 120 relationships and a scripted lookup would be far from ideal design choices.
This isn't just an issue for setting up a relationship to activities in order to show the name. Any reports where you list the scheduled activities, any searches for all registrants who have signed up for a given activity that can appear in multiple option fields will hit similar issues that can't be solved short of either a table redesign or incredibly cumbersome work arounds.