If I understand correctly, you have a record on the Coins layout and want to see the Mintage record specific for that Type and Year. Correct?
One method would be to place a portal to Mintage on your Coins layout and specify a portal filter to limit the related Mintage records to just the one for a specific year. Mintage::Year = Coins::Year might serve as that portal filter expression.
Another method is to enter Manage | Database | Relationships and use the duplicate button (two green plus signs) to create a duplicate of the Mintage table occurrence and link it to Coins directly:
Coins::year = Mintage 2::Year AND
Coins::TypeIDLink = Mintage 2::TypeID
Then you can add fields from Mintage 2 to your Coins layout or specify auto-enter options on Fields in the Coins table that copy data from fields in Mintage 2.
Note that Mintage 2 is not a duplicated table, it's a duplicated reference to the same table as the Mintage Tutorial: What are Table Occurrences? in your relationship graph.
You are correct in what I am trying to accomplish. As for method one, I presume it would be a one line portal with one field (mintage) with the portal filter you mention. For method two, when I add the Mintage2::Mintage field to the coins layout, I guess I need a refresh window when a Coin record loads? I am not sure what you mean by "specify auto-enter options" to copy data - the mintage data is informational only for reference - do you mean that it would actually copy information from the mintage table to a coin table field (which in this case I do not need that redundancy)?
From a performance (speed) perspective, which method do you think would work best?
when I add the Mintage2::Mintage field to the coins layout, I guess I need a refresh window when a Coin record loads?
That should not be required.
the mintage data is informational only for reference
Then you don't need any fields with auto-enter field options. Sometimes developers need to copy data from a related table, such as filling in line items on an invoice and using auto-enter options to copy the current prices from a related table. But that isn't what you need here from what I can tell.