Im not quite sure how to read ternary relationships within a ER-Diagram. Lets say this is the ternary relationship that is given. What can I interpret out of that?
Another late answer, but might serve future readers. But yes, you're correct @user2276094.
As you mentioned, multiplicities in ternary relationships are devised, by isolating one entity (a target entity) from the 2 other entities, and associating the target entity (say Staff) with a fixed pair of a single occurrence from the 2 other entities (say Client and Branch).
So, you can phrase those multiplicities in the relationship (says Staff register Client at a Branch) as,
For a fixed pair of a Staff occurrence, and a Branch occurrence, there may or may not be Clients (cause some staff may not register clients, they maybe involved in other duties).
For a fixed pair of a Branch occurrence, and a Client occurrence, there must be one and only Staff(cause a Client can be registered only once by one and only Staff member).
For a fixed pair of a Staff occurrence, and a Client occurrence, there must be one and only (assuming Client can be registered only at one branch).