Njegovo Veličanstvo može odobriti operaciju.

Because it agrees with Veličanstvo, which is a neuter singular noun in the nominative case.

The base possessive form is njegov = his, but like adjectives, Croatian possessives change their endings to match the noun they describe:

• masculine singular: njegov
• feminine singular: njegova
• neuter singular: njegovo

So Njegovo Veličanstvo is literally His Majesty, with njegovo matching the neuter noun Veličanstvo.

Because grammatical gender and real-world sex/gender are not the same thing.

In Croatian, Veličanstvo is grammatically a neuter noun, regardless of whether it refers to a king or a queen. Croatian agreement follows the noun’s grammatical gender, not the person’s biological sex.

So even for a king, you say:

• Njegovo Veličanstvo

And for a queen:

• Njezino Veličanstvo

In both cases, Veličanstvo stays neuter.

It is in the nominative case because it is the subject of the sentence.

In this sentence, Njegovo Veličanstvo is the one performing the action of može odobriti.

So the structure is:

• Njegovo Veličanstvo = subject
• može odobriti = verb phrase
• operaciju = direct object

Može is the 3rd person singular present tense of moći, meaning can, may, or is able to.

Depending on context, može can express:

• ability
• possibility
• permission
• authority

In this sentence, the most natural sense is probably has the authority to or may approve the operation, though can approve is also a valid translation.

Because after the modal verb moći, Croatian uses the infinitive of the main verb.

So:

• može odobriti = can/may approve

This is similar to English can approve, except Croatian does not use a separate word like to here.

You do not say something like može odobrava in this structure. After moći, the normal pattern is:

• moći + infinitive

Examples:

• Može doći = He/She can come
• Može pomoći = He/She can help
• Može odobriti = He/She can approve

Because operaciju is the accusative singular form of operacija.

Here, operaciju is the direct object of the verb odobriti. It is the thing being approved.

For many feminine nouns ending in -a, the accusative singular changes to -u:

• operacija → operaciju
• knjiga → knjigu
• odluka → odluku

So:

• operacija = dictionary form, nominative
• operaciju = accusative form, used as the object

No. Croatian word order is fairly flexible because case endings show grammatical roles.

The sentence as given:

• Njegovo Veličanstvo može odobriti operaciju.

is a neutral, natural order.

But other orders are possible for emphasis, for example:

• Operaciju može odobriti Njegovo Veličanstvo.
  This emphasizes who can approve it.

• Njegovo Veličanstvo operaciju može odobriti.
  Also possible, though less neutral.

Even when the order changes, the case endings still tell you that operaciju is the object and Njegovo Veličanstvo is the subject.

Because it is being used as a formal honorific title.

In respectful or official usage, Croatian often capitalizes words like this when referring to someone with high status, especially in ceremonial or formal contexts.

So Njegovo Veličanstvo works like a set title, similar to His Majesty in English.

You may sometimes see variation depending on style and context, but capitalization here clearly signals a formal title.

You would say:

Njezino Veličanstvo može odobriti operaciju.

Only the possessive changes:

• Njegovo = his
• Njezino = her

But the ending -o stays because it still has to agree with the neuter noun Veličanstvo.

Not only that. Odobriti can also mean things like:

• approve
• authorize
• grant
• sanction

The best English choice depends on context.

For example:

• odobriti zahtjev = approve a request
• odobriti sredstva = allocate/approve funds
• odobriti operaciju = approve/authorize an operation

So in this sentence, approve is a very natural translation, but authorize might also fit depending on the situation.