Ne induljatok el anélkül, hogy ellenőriznétek a szélirányt!

Because ne is the negative particle used with commands and other imperative/subjunctive forms.

• nem negates ordinary statements
  
  • Nem indultok el. = You are not setting off.
• ne negates commands
  
  • Ne induljatok el! = Don’t set off!

So in this sentence, Ne is exactly what you expect before a negative command.

Induljatok is the 2nd person plural imperative form of indulni = to start / to set off / to depart.

It is used when speaking to more than one person:

• indulj = set off! (to one person)
• induljatok = set off! (to several people)

So Ne induljatok el! means Don’t set off! addressed to a group.

Because el is a preverb, and Hungarian preverbs often change position depending on the sentence type.

The dictionary form is elindulni, but in an imperative the preverb normally comes after the verb:

• Induljatok el! = Set off!

With negation, preverbs also stay separate:

• Ne induljatok el! = Don’t set off!

So although the full verb is elindulni, the sentence naturally appears as induljatok el here.

Hungarian usually drops subject pronouns when the verb ending already shows the person and number.

Here, both verb forms already tell you the subject is you plural:

• induljatok = you all set off
• ellenőriznétek = you all would check

So adding ti would usually only be for emphasis or contrast:

• Ti ne induljatok el... = You don’t set off...

Without emphasis, leaving out ti is the normal choice.

Anélkül, hogy is a very common Hungarian structure meaning without doing something.

In this sentence:

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

But together, anélkül, hogy functions as the natural Hungarian equivalent of English without + -ing:

• anélkül, hogy ellenőriznétek a szélirányt
  = without checking the wind direction

Hungarian often uses a finite clause here, where English would often use just a gerund:

• English: without checking
• Hungarian: anélkül, hogy ... ellenőriznétek

Because Hungarian is introducing a subordinate clause.

English can say:

• without checking the wind direction

But Hungarian normally says the equivalent of:

• without [the fact] that you check the wind direction

That is why hogy appears: it introduces the clause after anélkül.

So this pattern is standard:

• anélkül, hogy + verb

You should learn it as a set expression.

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

So even though ellenőriznétek literally looks like you would check, in this structure it simply helps express:

• without checking

This is a normal grammatical pattern, not a special nuance of politeness or uncertainty.

A good way to remember it is:

• anélkül, hogy + conditional verb
  = without doing something

So:

• anélkül, hogy ellenőriznétek...
  = without checking...

It can be broken down like this:

• ellenőriz- = verb stem, check
• -né- = conditional marker
• -tek = you plural

So:

• ellenőriznétek = you (plural) would check

In this sentence, that conditional form is used because of the anélkül, hogy structure.

A detail that sometimes confuses learners: this verb has a definite object here, but in the 2nd person plural conditional, the definite and indefinite forms happen to look the same, so ellenőriznétek is exactly the form you expect.

Because szélirányt is the direct object of ellenőriznétek.

• szélirány = wind direction
• szélirányt = wind direction + accusative -t

Hungarian marks direct objects with -t.

So:

• ellenőriznétek a szélirányt
  = you would check the wind direction

The article a makes it definite: the wind direction.

Yes, this word order is completely natural.

The sentence has a neutral, standard structure:

• Ne induljatok el = main command
• anélkül, hogy ellenőriznétek a szélirányt = subordinate clause explaining what must happen first

Hungarian word order is flexible, but changes usually add emphasis or focus. This version sounds straightforward and idiomatic.

For example, you could emphasize the object:

• ...hogy a szélirányt ellenőriznétek

But the original sentence is the most neutral and natural way to say it.