In Civilization 6 the rules for district yields sound clear from the manual, but in practice it seems like they are different.
In the manual, yields seem to be based on 1) adjacency bonus, 2) buildings in the district (these are shown separately if you look at the resource breakdown for the city), 3) specialists assigned to work the district (2 resources per specialist).
But the below Holy Site has a very different story. In the resources breakdown for the city it shows +6 faith for the Holy Site. This doesn't make any sense to me, because based on adjacency bonuses I should have +2 (or +2.5): 1 for the mountain, 1 for the rainforest because I have the Sacred Path pantheon belief, and maybe 0.5 for the adjacent Holy Site from a different city (I don't know if the districts of other cities are counted or if half a point counts).
Separately the breakdown shows +2 for Specialists, but I assume this is separate. Even if it were combined, that doesn't explain how it shows +6.
I do have the Simultaneum policy that doubles faith output from Holy Site district buildings, but buildings are listed separately. For the record my building outputs are +4 Shrine, +8 Temple, +6 Gurdwara. I also have the Triangular Trade policy that provides +1 faith for each trade route, but this city has no trade routes.
I also don't know how to interpret the 1 and 3 that are overlayed on the district in the image. However I think it means I have space for 3 specialists here, but only 1 is assigned (hence the +2 from Specialists).
Incidentally, it would be really nice for choosing policies if the game provided a way to lookup adjacency bonuses once a district is already built.
Best Answer
The extra 4 faith is probably from envoys at religious city states. If you have 3 envoys at a religious city state, you get +2 faith per holy site. If you have 6 envoys at a religious city state, you get an additional +2 faith per holy site (for a total of 4).
So, your 6 would be 1 for the mountain, 1 for the sacred path rainforest, and 4 for city states.
Also, while districts in other cities count for the adjacency bonus, there are no half points for adjacency bonuses that require 2 adjacent tiles. And also, you cannot combine 2 different bonuses. For example, with holy sites, 1 adjacent forest and 1 adjacent district gets you 0 faith in adjacency.