Si tu ne comprends pas, je peux te l’expliquer une deuxième fois.

After si meaning if, French normally uses the present tense, not the future, for a real possible condition.

So:

• Si tu ne comprends pas = If you don’t understand
• not si tu ne comprendras pas

This is a very common French pattern:

• Si tu viens, je serai content.
• If you come, I’ll be happy.

French uses:

• present after si
• often future / present / imperative in the main clause, depending on meaning

In your sentence, both verbs are in the present:

• tu ne comprends pas
• je peux

That makes the whole sentence sound natural and conversational.

Ne ... pas is the standard way to make a verb negative in French.

So:

• tu comprends = you understand
• tu ne comprends pas = you do not understand / you don’t understand

It goes around the conjugated verb:

• ne before the verb
• pas after the verb

With comprends:

• tu ne comprends pas

In everyday spoken French, people often drop ne:

• Si tu comprends pas...

But in normal written French, and in careful speech, ne ... pas is the standard form.

Because the verb is comprendre and here it is conjugated for tu in the present tense.

Present tense of comprendre:

• je comprends
• tu comprends
• il/elle comprend
• nous comprenons
• vous comprenez
• ils/elles comprennent

So tu comprends means you understand.

The s is just part of the normal tu form for this verb.

Te means to you here.

The verb expliquer often works like this:

• expliquer quelque chose à quelqu’un
• to explain something to someone

So in this sentence:

• the something is represented by l’
• the to someone is represented by te

So:

• je peux te l’expliquer literally = I can explain it to you

Even though te looks like you, in this sentence it corresponds to to you.

L’ is a direct object pronoun meaning it.

It stands for whatever is being explained:

• a rule
• a word
• a sentence
• an idea
• etc.

For example:

• Je peux expliquer la règle. = I can explain the rule.
• Je peux l’expliquer. = I can explain it.

It becomes l’ instead of le or la because the next word starts with a vowel:

• l’expliquer

So l’ can stand for:

• le
• la

depending on the noun it replaces.

French object pronouns have a fixed order, and when they go with an infinitive, they usually come before the infinitive.

Here the verb structure is:

• peux expliquer = can explain

The pronouns belong to expliquer, so they go right before it:

• te l’expliquer

The normal order is:

1. me / te / se / nous / vous
2. le / la / les
3. lui / leur
4. etc.

So:

• te comes before l’

That is why:

• je peux te l’expliquer is correct

Not:

• je peux l’te expliquer
• je peux expliquer te le

Because peux is just the conjugated modal verb pouvoir (can), and the real action is in the infinitive expliquer.

In French, object pronouns usually go before the verb they belong to. Here they belong to expliquer, not really to peux.

So:

• Je peux expliquer cela à toi becomes
• Je peux te l’expliquer

This is the same pattern you see in sentences like:

• Je vais le faire. = I’m going to do it.
• Je veux te parler. = I want to talk to you.

The pronoun sits before the infinitive:

• le faire
• te parler
• te l’expliquer

Yes. If you are speaking formally or to more than one person, you would use vous instead of tu.

That gives:

• Si vous ne comprenez pas, je peux vous l’expliquer une deuxième fois.

So the difference is mainly:

• tu / te / comprends = informal singular
• vous / vous / comprenez = formal singular or plural

The original sentence is informal and friendly.

Because French uses the expression une fois for one time / once / an occasion of doing something, and then modifies it with an ordinal number.

So:

• une première fois = a first time
• une deuxième fois = a second time
• une troisième fois = a third time

Here:

• une agrees with fois
• fois is feminine

So une deuxième fois literally means a second time.

They are similar, but not exactly the same.

• une deuxième fois = a second time
• encore une fois = again / one more time

In many situations they can both work, but the nuance changes:

• Je peux te l’expliquer une deuxième fois.
  Emphasis: this would be the second explanation.

• Je peux te l’expliquer encore une fois.
  Emphasis: I can explain it again.

If you specifically mean for the second time, une deuxième fois is more precise.

Mostly yes, but the French structure is worth noticing.

French often uses:

• expliquer quelque chose à quelqu’un

Examples:

• J’explique la leçon à Marie.
• I explain the lesson to Marie.

When pronouns replace those objects:

• la leçon → la / l’
• à Marie → lui
• à toi → te

So:

• Je te l’explique. = I explain it to you.

That is exactly the pattern used in your sentence.

Je peux simply means I can or I’m able to. In this sentence it sounds polite and helpful:

• If you don’t understand, I can explain it to you a second time.

Other choices are possible, but they change the tone:

• Je vais te l’expliquer...
  = I’m going to explain it...
  More direct; it sounds like the speaker has decided to do it.

• Je peux te l’expliquer...
  = I can explain it...
  Softer; it offers help.

• Je peux aussi te l’expliquer...
  = I can also explain it...
  Adds the idea of also, which is not present in the original.

So je peux is a natural choice for an offer.

Yes. The French present tense is flexible, just like the English present in many contexts.

Here, tu ne comprends pas can mean:

• if you don’t understand
• if you’re not understanding
• if it isn’t clear to you

The exact nuance depends on context, but in this sentence it naturally means something like:

• If you don’t understand, I can explain it to you again.

So it does not have to mean a broad, permanent lack of understanding. It can refer to the current situation.

Yes, it is natural and correct.

It sounds:

• polite
• helpful
• conversational

A native speaker might also say things like:

• Si tu ne comprends pas, je peux te réexpliquer.
• Si tu ne comprends pas, je peux te l’expliquer encore une fois.
• Si ce n’est pas clair, je peux te l’expliquer une deuxième fois.

But your sentence is completely normal French.