Большой собаке нужен намордник, если мы едем с ней в метро.

Because Russian uses the pattern кому? нужен что? for someone needs something.

So in:

Большой собаке нужен намордник

the dog is not the grammatical subject in the same way it would be in English. Literally, the structure is closer to:

• To the big dog, a muzzle is needed

That is why собака becomes собаке: it is in the dative singular.

Нужен agrees with the thing that is needed, not with the person or animal who needs it.

Here, the thing needed is намордник (muzzle), and намордник is:

• masculine
• singular

So the correct form is нужен.

Compare:

• Собаке нужен намордник. = The dog needs a muzzle.
• Собаке нужна вода. = The dog needs water.
• Собаке нужно место. = The dog needs space.
• Собаке нужны лекарства. = The dog needs medicines.

Because большой has to agree with собаке.

Since собаке is:

• feminine
• singular
• dative

the adjective must also be:

• feminine
• singular
• dative

So:

• nominative: большая собака
• dative: большой собаке

This is adjective agreement.

After the preposition с meaning with, Russian uses the instrumental case.

The pronoun она changes like this:

• nominative: она = she
• genitive/accusative: её
• dative: ей
• instrumental: ней
• prepositional: ней

So:

• с ней = with her

That is why с она is impossible here, and с её would also be wrong.

After many prepositions, Russian third-person pronouns add н- at the beginning.

So you get:

• у неё
• к нему
• с ней
• о них

Without a preposition, you usually do not add that н:

• ей
• ему
• ими

So с ней is the normal and expected form.

Russian usually distinguishes between:

• идти / ходить = to go on foot
• ехать / ездить = to go by vehicle

Since the sentence says в метро, we are traveling by transport, so едем is the right choice.

• Мы едем в метро. = We are going by metro.
• Мы идём в метро. = We are walking to the metro / into the metro station, depending on context.

So едем specifically tells you the trip is by train/transport.

Если мы едем is a normal way in Russian to express a general condition or repeated situation:

• if we are going / if we ride / when we go

It works well for rules, habits, or typical situations.

So this sentence sounds like a general rule:

• A big dog needs a muzzle if we go with her on the metro.

If you said если мы будем ехать, that would sound more like a specific future situation:

• if we are going to be riding

That is possible in some contexts, but here the present-tense form is the most natural for a general statement.

Because метро is one of the Russian nouns that are normally indeclinable.

That means its form does not change across cases:

• метро
• в метро
• из метро
• к метро

So even though в often requires a different case form, the word itself stays the same.

Here в метро uses the prepositional case meaning, because it means in the metro / on the metro as a location or setting.

With в, Russian often contrasts:

• в + accusative = motion into
• в + prepositional = location inside / in

Examples:

• Мы идём в метро. = We are going into the metro.
• Мы едем в метро. = We are riding in the metro.

Even though метро does not change its form, the grammatical case idea is still there.

It can mean either, depending on context.

Russian has no articles like a and the, so:

• Большой собаке нужен намордник

could mean:

• A big dog needs a muzzle
• The big dog needs a muzzle

The surrounding context tells you which one is intended.

No. Russian has several ways to express this idea.

In this sentence, нужен is a very natural choice for someone needs something.

Another common option is the verb нуждаться в + prepositional:

• Собака нуждается в наморднике.

But that sounds more formal or bookish in many contexts.

So for everyday speech, собаке нужен намордник is usually more natural.

Yes. Russian word order is flexible, and changing it can shift emphasis.

The given sentence:

• Большой собаке нужен намордник, если мы едем с ней в метро.

is perfectly natural.

You could also say:

• Если мы едем с ней в метро, большой собаке нужен намордник.
• Намордник нужен большой собаке, если мы едем с ней в метро.

These all mean basically the same thing, but the focus changes slightly.

• starting with если... highlights the condition first
• starting with намордник emphasizes the muzzle
• starting with большой собаке emphasizes the dog

Намордник means muzzle — the device put over a dog’s mouth/snout to prevent biting.

It is a masculine noun, which is why the sentence has:

• нужен намордник

and not нужна or нужно.

Both orders are possible:

• с ней в метро
• в метро с ней

In this sentence, едем с ней в метро sounds very natural and groups the idea as:

• we go with her
• by metro / on the metro

If you say едем в метро с ней, it is also understandable, but the rhythm and emphasis are a little different. Russian often allows both, especially in longer phrases like this.