Мы сдвинули шкаф и нашли тайный ход.

A word-by-word breakdown is:

• Мы = we
• сдвинули = moved / shifted
• шкаф = wardrobe / cabinet / cupboard
• и = and
• нашли = found
• тайный = secret / hidden
• ход = passage / entrance / way through

So the sentence is literally something like:

We moved the wardrobe and found a secret passage.

Yes, Russian often can leave out subject pronouns when they are understood from the verb form.

So both of these are possible:

• Мы сдвинули шкаф и нашли тайный ход.
• Сдвинули шкаф и нашли тайный ход.

The verb endings already show that the subject is we because both сдвинули and нашли are past plural forms.

Including мы makes the subject more explicit. It can sound more natural if you want to emphasize we specifically, especially in a story.

Сдвинули is:

• past tense
• plural
• from the verb сдвинуть = to move / shift something

Because it is plural, it agrees with мы.

Compare:

• я сдвинул / сдвинула = I moved
• ты сдвинул / сдвинула = you moved
• он сдвинул = he moved
• она сдвинула = she moved
• мы сдвинули = we moved
• они сдвинули = they moved

In the past tense, Russian verbs show gender in the singular but not in the plural.

This is about aspect, which is very important in Russian.

• сдвинули is perfective
• двигали would be imperfective

Here, the sentence describes a completed action with a result:

• they moved the wardrobe
• as a result, they found a secret passage

So сдвинули is the natural choice.

A rough contrast:

• мы двигали шкаф = we were moving the wardrobe / used to move the wardrobe / moved it around
  This focuses on the process.
• мы сдвинули шкаф = we moved the wardrobe (successfully, as a completed action)
  This focuses on the result.

Because the next action is нашли (found), the completed sense fits very well.

It is in the accusative case, but for many inanimate masculine nouns, the accusative looks exactly the same as the nominative.

So:

• nominative: шкаф
• accusative: шкаф

That is why the form does not visibly change.

This is normal for masculine inanimate nouns:

• вижу стол = I see a table
• открыл шкаф = opened the wardrobe
• сдвинули шкаф = moved the wardrobe

If the noun were animate, the accusative would often look different.

Because тайный ход is the direct object of нашли, so it is in the accusative case.

But both words are masculine singular inanimate, and for that pattern the accusative looks like the nominative:

• тайный stays тайный
• ход stays ход

So:

• nominative: тайный ход
• accusative: тайный ход

The adjective must agree with the noun in:

• gender
• number
• case

Here they match perfectly: masculine, singular, accusative/inanimate form.

In this sentence, ход does not mean just movement in the abstract.

Here, тайный ход means something like:

• secret passage
• hidden passageway
• secret entrance

Russian ход can have several meanings depending on context, such as:

• movement
• way of proceeding
• turn in a game
• passage / way through

In adventure or mystery contexts, тайный ход is a very common expression for a hidden passage.

Both тайный and секретный can relate to the idea of secret, but they are not always used in exactly the same way.

In this context, тайный ход is the standard, natural phrase for secret passage.

A useful distinction:

• тайный = hidden, secret, concealed
• секретный = secret, confidential, classified

Examples:

• тайная дверь = hidden/secret door
• тайный ход = secret passage
• секретный документ = classified document
• секретная информация = secret information

So тайный ход sounds more idiomatic here.

Нашли is:

• past tense
• plural
• from найти = to find
• perfective

It is used because the sentence refers to a completed discovery: they found the passage.

Compare:

• находили = were finding / used to find / found repeatedly
• нашли = found (successfully, as a completed fact)

In a sequence of story events, perfective past verbs are very common:

• сдвинули = moved
• нашли = found

That gives the sentence a clear narrative progression.

Yes. Russian word order is more flexible than English because case endings help show the grammatical roles.

The neutral order here is:

• Мы сдвинули шкаф и нашли тайный ход.

But other orders are possible, for example:

• Шкаф мы сдвинули и нашли тайный ход.
• Тайный ход мы нашли, сдвинув шкаф.

Changing the order usually changes emphasis, not the basic meaning.

The original version is the most straightforward and natural for a simple narrative sentence.

Russian has no articles.

So:

• шкаф can mean the wardrobe or a wardrobe
• тайный ход can mean a secret passage or the secret passage

The exact meaning depends on context.

In this sentence, English naturally uses:

• the wardrobe if it is already known in the story
• a secret passage if it is being mentioned for the first time

Russian leaves that distinction to context instead of using articles.

A rough pronunciation guide is:

My sdVEE-nu-li shkaf ee nash-LI TAI-ny khot

A few notes:

• ы in мы is a Russian vowel with no exact English equivalent
• ш in шкаф is like sh
• х in ход is like the ch in Scottish loch or German Bach
• stress:
  • мы
  • сдвИнули
  • шкаф
  • и
  • нашлИ
  • тАйный
  • ход

A more standard transliteration would be:

My sdvinuli shkaf i nashli taynyy khod.