Use 'tuyo' when speaking in 2nd person (tú). Use 'suyo' when speaking in 3rd person (usted, él, ella). Please note that both 'tuyo' and 'suyo' can mean 'your'. 'suyo' is simply more formal.
Also, both are possessive pronouns and so stand alone. Example: 'Este libro es suyo' = 'This book is YOURS'. In contrast 'su' is a possessive adjective and cannot stand alone. Example: 'Es su libro' = 'It is YOUR BOOK'.
I try to listen more than read most of the examples. This example did not have the inflection of a question. I wrote "Sir, this coat is yours" because the speaker did not speak it as a question. I guess I'll have to read to check before submitting an answer. ( not the first time this has happened)
This highlights a (possibly regional?) issue in English.
Although from Spanish we usually understand «señor» to equate to "sir" and «caballero» to mean "gentleman", it is uncommon in most parts of the world to pluralise the English "sir" as "sirs".
Both would become "gentlemen".
Similarly you do not see "madams" but "ladies".
Spanish, of course, is fine with «señores» and «caballeros».
Okay, I understand that Duolingo is speaking more in terms of acceptable English than acceptable Spanish now. Do we never use sirs to mean gentlemen? Although I would agree that it is uncommon, it is occasionally used, and therefore, I would submit it is not incorrect in English in general.
I think duolingo has made a rod for it's back by putting "señor" / "señora etc before the question because unless you are in a formal situation i.e. hotel porter / cloakroom butler etc you would just say "is this cost yours" or "excuse me, is this coat yours ?" Their phrase has created a lot of problems and shows how quirky English is. Much more simple to say Señor or senores for single or plural. If, however you were that butler or be in a formal situation of returning coats to a man or group of men, you would say "gentlemen" or "gents"to a group of men, never "sirs". To an individual man you would say "sir" and never "gentleman" or 'gent". We would begin a speech to a group of people with "Ladies and Gentlemen". I believe a Spaniard may start with Senores y Senoras ? Either way we wouldn't say Ma'ams and sirs !!