Lemondjuk a foglalást anélkül, hogy beszélnénk a recepcióssal.

Because a foglalást is a definite direct object: it means the reservation / this specific reservation.

Hungarian verbs often have two conjugation patterns:

• indefinite conjugation: used when there is no definite object
• definite conjugation: used when the object is definite

So:

• Lemondunk egy foglalást. = We cancel a reservation.
• Lemondjuk a foglalást. = We cancel the reservation.

The ending -juk shows the definite conjugation for mi = we.

The -t is the accusative ending, which marks the direct object of the verb.

Here, the thing being canceled is the reservation, so foglalás becomes foglalást.

• foglalás = reservation
• foglalást = reservation (as the object)

Because it has the article a, the full object is a foglalást.

Anélkül, hogy is a very common Hungarian structure meaning without doing something or without the fact that...

In this sentence:

• anélkül = without that / without it
• hogy = that

But you should learn anélkül, hogy as a fixed pattern, because together it functions like English without + verb.

So:

• anélkül, hogy beszélnénk a recepcióssal
  = without speaking to the receptionist

It is one of those expressions that is best understood as a unit, not translated word by word too literally.

After anélkül, hogy, Hungarian normally uses the conditional form.

So even though English says without speaking, Hungarian says something closer to:

• without that we would speak...

That is why you get:

• beszélnénk = we would speak

This is standard grammar after anélkül, hogy.

A similar pattern:

• Elment anélkül, hogy szólt volna.
  = He left without saying anything.

So the conditional here does not mean a real condition like if. It is just the normal form used in this construction.

Because the structure requires it.

After anélkül, hogy, Hungarian usually uses:

• a finite verb
• in the conditional
• matching the subject

Here the main verb is lemondjuk = we cancel, so the implied subject is we.
Therefore the second verb also matches we:

• beszélnénk = we would speak

So:

• beszélünk = we speak
• beszélni = to speak
• beszélnénk = we would speak

Only beszélnénk fits this pattern.

The ending -val / -vel means with.

So:

• recepciós = receptionist
• recepcióssal = with the receptionist

The reason it becomes -sal instead of a separate -val is assimilation. In Hungarian, -val/-vel often changes to match the final consonant of the word.

Since recepciós ends in s, the v disappears and the s is doubled:

• recepciós + val → recepcióssal

This is very normal in Hungarian:

• fiúval = with the boy
• tanárral = with the teacher
• kézzel = with a hand
• recepcióssal = with the receptionist

Hungarian uses beszél valakivel for speak with/to someone.

So:

• beszélni valakivel = to speak with someone / to speak to someone

English often prefers to in this situation, but Hungarian uses the suffix meaning with.

Compare:

• Beszélek a tanárral. = I’m speaking to the teacher.
• Beszélnénk a recepcióssal. = We would speak to/with the receptionist.

So this is completely natural Hungarian usage.

Because Hungarian usually does not need subject pronouns unless they are emphasized.

The verb ending already shows the subject:

• lemondjuk = we cancel it
• beszélnénk = we would speak

So adding mi is unnecessary unless you want emphasis or contrast:

• Mi mondjuk le a foglalást... = We are the ones canceling the reservation...

Most of the time, Hungarian leaves the pronoun out.

Le- is a verbal prefix. Hungarian uses many prefixes to change or specify the meaning of verbs.

The base verb mond means say.
But lemond is a separate verb meaning cancel, call off, or renounce, depending on context.

So here you should learn:

• lemond valamit = to cancel something

Examples:

• Lemondom az utat. = I cancel the trip.
• Lemondjuk a foglalást. = We cancel the reservation.

So the meaning is not just say down or anything literal like that. It is a standard prefixed verb with its own meaning.

Yes. Hungarian word order is fairly flexible, and changing it often changes focus or emphasis, not the basic meaning.

The sentence as given is neutral and natural:

• Lemondjuk a foglalást anélkül, hogy beszélnénk a recepcióssal.

But other versions are possible, for example:

• Anélkül mondjuk le a foglalást, hogy beszélnénk a recepcióssal.
• A foglalást mondjuk le anélkül, hogy beszélnénk a recepcióssal.

These would sound more marked, with different emphasis.

For a learner, the given order is a very good default.

It is the person we speak to/with.

In Hungarian:

• beszélni valakivel = speak with someone
• beszélni valamiről = speak about something

So:

• a recepcióssal = with the receptionist
• if it were about the receptionist, it would be something like a recepciósról

That distinction is important:

• Beszélünk a recepcióssal. = We speak to the receptionist.
• Beszélünk a recepciósról. = We speak about the receptionist.

Yes, it is natural and grammatically standard.

The pattern

• anélkül, hogy + conditional verb

is one of the main ways Hungarian expresses without doing something.

So this sentence is a good model to learn from.

A similar example:

• Elmentem anélkül, hogy ettem volna.
  = I left without eating.

So if you want to say without calling, without asking, without speaking, this structure is very useful.