Questions & Answers about Его ответ был убедительным.
Here его means his because it directly modifies the noun ответ.
The same form его can also mean him in other sentences, but here the structure makes it clearly possessive:
- его ответ = his answer
A useful thing to remember: Russian third-person possessives его, её, and их do not change to match the noun they go with:
- его ответ
- его книга
- его письма
All of those still use его.
Ответ is the subject of the sentence, so it is in the nominative singular.
The sentence is about the answer, and that is the thing described as convincing. So the basic structure is:
- ответ = subject
- был = was
- убедительным = convincing
The dictionary form is also ответ.