Quand le professeur explique la règle avec un exemple simple, tout prend enfin du sens.

Here quand means when in a general, habitual sense.

The sentence is not talking about one single event only. It means something like: whenever the teacher explains the rule with a simple example, everything finally makes sense.

French quand can work for both:

• a specific moment: Quand il est arrivé, tout a changé.
• a general situation: Quand le professeur explique bien, les élèves comprennent.

So in this sentence, quand introduces the condition or circumstance under which everything becomes clear.

Yes, lorsque would be grammatically correct:

Lorsque le professeur explique la règle avec un exemple simple, tout prend enfin du sens.

The difference is mostly one of style:

• quand is more common and everyday
• lorsque is a bit more formal or literary

In normal speech, quand is the most natural choice.

Le professeur means the teacher, so it refers to a specific teacher or to the teacher in the situation being discussed.

If you said un professeur, it would mean a teacher, which is more indefinite:

• Le professeur explique la règle... = the teacher explains the rule...
• Un professeur explique la règle... = a teacher explains the rule...

French often uses the definite article where English also uses the, especially when the person is already understood from context.

French uses the present tense here because the sentence expresses:

• a general truth
• a repeated situation
• something that typically happens

So Quand le professeur explique... means When the teacher explains... / Whenever the teacher explains...

French does this very often with quand, si, and similar structures:

• Quand il parle lentement, je comprends mieux.
• Si tu étudies, tu progresses.

Even though English sometimes sounds more natural with when the teacher explains, French just uses the ordinary present tense.

In French, nouns usually need an article or determiner. So you normally say:

• la règle = the rule
• une règle = a rule
• cette règle = this rule

You generally cannot leave a singular countable noun bare the way English sometimes can in certain expressions.

So explique la règle is the normal way to say explains the rule.

Avec un exemple simple means with a simple example.

It tells you how the teacher explains the rule. So it goes with explique:

• explique la règle avec un exemple simple = explains the rule using a simple example

It does not mean that the rule itself is simple. The adjective simple describes exemple, not règle.

Both are possible, but they do not mean exactly the same thing.

• un exemple simple = a simple example
  This means the example itself is easy or straightforward.

• un simple exemple = a mere example / just an example
  Here simple often means mere or only, not easy.

So in your sentence, un exemple simple is the correct choice because the idea is that the teacher uses an easy, clear example.

Here tout means everything.

It is a singular subject, so the verb is singular:

• tout prend not
• tout prennent

This tout is a pronoun, not an adjective. It stands on its own and means everything / all of it.

Compare:

• Tout va bien. = Everything is going well.
• Tout prend du sens. = Everything starts to make sense.

Yes, prendre du sens is a very common expression.

It means:

• to make sense
• to start making sense
• to become meaningful / understandable

Literally, prendre means to take, but you should learn prendre du sens as a whole expression.

Examples:

• Peu à peu, cette théorie prend du sens.
• Après son explication, tout prend du sens.

French often uses verbs in expressions where English uses something less literal.

In prendre du sens, the du is part of the fixed expression.

Here du is the partitive article, roughly like some in English, though English usually does not say it explicitly. The idea is something like to take on meaning / to make sense.

So:

• prendre du sens = to make sense / to acquire meaning

You normally would not say prendre le sens in this meaning. That would suggest take the meaning, which is something different.

So the safest approach is to memorize:

• avoir du sens = to make sense
• prendre du sens = to start making sense / become meaningful

Good question. Both are common, but they are not identical.

• avoir du sens = to make sense
  This describes a state.

  • Cette explication a du sens.

• prendre du sens = to start making sense / to become meaningful
  This suggests a change or development.

  • Tout prend du sens après l'exemple.

In your sentence, prend enfin du sens is especially natural because enfin suggests that things were unclear before, and now they are becoming clear.

Enfin means finally.

It adds the idea that understanding comes after some difficulty, confusion, or delay. So:

• without enfin: everything makes sense
• with enfin: everything finally makes sense

It suggests relief:

• at first, the rule was confusing
• then the teacher gives a simple example
• now everything becomes clear

So enfin is doing important emotional and logical work in the sentence.

The comma is natural and standard here because the sentence begins with a subordinate clause:

Quand le professeur explique la règle avec un exemple simple, tout prend enfin du sens.

The first part sets the situation, and the second part gives the main result. French often uses a comma after an introductory clause like this, especially when the clause is long enough.

If you reverse the order, you would usually not need the comma:

• Tout prend enfin du sens quand le professeur explique la règle avec un exemple simple.

Both word orders are correct.

Yes:

Tout prend enfin du sens quand le professeur explique la règle avec un exemple simple.

This means the same thing overall. The difference is one of emphasis:

• starting with Quand... highlights the condition or situation first
• starting with Tout prend enfin du sens... highlights the result first

Both are natural. The original version is slightly more descriptive and smooth in tone.

You could, but the meaning and tone change slightly.

• professeur is the usual word for teacher, especially in school contexts
• enseignant means teacher too, but it is often more formal or administrative, closer to teaching staff member or educator

So in an everyday sentence like this, le professeur sounds very natural.

Also, in modern French, prof is the common informal short form:

• Quand le prof explique la règle...

But that is more casual than le professeur.

Yes. Adjectives in French usually agree with the noun they describe.

Here:

• exemple is masculine singular
• so the adjective is also masculine singular: simple

That is why you get:

• un exemple simple

If the noun were feminine singular:

• une explication simple

If it were masculine plural:

• des exemples simples

If it were feminine plural:

• des règles simples