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.

In the past tense, Russian verbs agree with the subject in gender and number.

Since ответ is masculine singular, the verb must be был.

Compare:

• ответ был — the answer was
• книга была — the book was
• письмо было — the letter was
• ответы были — the answers were

So был is used because ответ is masculine singular.

Russian usually leaves out the present-tense verb to be.

So in the present, you often get:

• Его ответ убедителен = His answer is convincing

But in the past, Russian does use forms of быть:

• Его ответ был убедительным = His answer was convincing

So:

• present: usually no is
• past: был / была / было / были

Because after был with a full adjective used as the predicate, Russian normally puts that adjective in the instrumental.

So:

• Он был добрым = He was kind
• Она была счастливой = She was happy
• Его ответ был убедительным = His answer was convincing

Here убедительным is the instrumental singular masculine form of убедительный.

This is one of the most common patterns learners meet after forms of быть in the past tense.

Yes, you could.

That version uses the short-form adjective убедителен instead of the full form убедительным.

Both are correct:

• Его ответ был убедительным
• Его ответ был убедителен

The difference is mostly stylistic:

• был убедительным = neutral and very common
• был убедителен = a bit more formal, compact, or bookish

The meaning is basically the same here.

The dictionary form is убедительный.

Its form here, убедительным, is:

• singular
• masculine
• instrumental

It comes from the verb убедить, meaning to convince.

So the adjective literally has the idea of able to convince or convincing.

Yes. Russian word order is flexible, because the endings carry much of the grammar.

The most neutral version is:

• Его ответ был убедительным.

But you could also say:

• Ответ его был убедительным.
• Убедительным был его ответ.

These alternatives change the emphasis or sound more literary, but the core meaning stays the same.

A natural stress pattern is:

егó отвéт был убедúтельным

A rough pronunciation guide:

• его ≈ yi-VO
• ответ ≈ at-VYET
• был ≈ byl
• убедительным ≈ oo-bee-DEE-tyel-nym

A couple of useful notes:

• In его, the г is pronounced like v: егó
• Unstressed о often sounds closer to a
• Russian stress is important and must often be memorized word by word

Свой is usually used when the possessor is the same as the subject of the clause.

In this sentence, the grammatical subject is ответ, so свой does not work the same way here. Его ответ simply means his answer.

You can see the difference more clearly in bigger sentences:

• Он дал свой ответ. = He gave his own answer.
• Я слышал его ответ. = I heard his answer.

So in your sentence, его is the natural choice.