Die buurman vra of hy my boek kan leen, maar hy belowe om dit vanaand terug te gee.

Die is the Afrikaans definite article, meaning the.

So:

• die buurman = the neighbor
• buurman = neighbor in a more general or indefinite sense

A useful thing to remember is that Afrikaans uses die for the in all genders and in plural too, so it is much simpler than English learners often expect.

Here vra ... of means asks if / asks whether.

So:

• Die buurman vra of ... = The neighbor asks if / whether ...

The word of in this sentence does not mean or. In this structure, it introduces an indirect yes/no question.

Compare:

• Hy vra of hy kan kom. = He asks if he can come.

Because of introduces a subordinate clause, and subordinate clauses in Afrikaans usually push the verb group toward the end.

So instead of an English-like order, Afrikaans gives you:

• of
  • subject + other information + verb(s) at the end

Here that becomes:

• of hy my boek kan leen

Breakdown:

• hy = he
• my boek = my book
• kan leen = can borrow

This end-position for the verbs is very common after words like of, dat, omdat, etc.

This is because kan is a modal verb, and leen is the main verb.

• kan = can
• leen = borrow

In Afrikaans, when a modal verb is used inside a subordinate clause, both verbs normally go to the end:

• ... of hy my boek kan leen

This is similar to other Germanic languages like Dutch and German.

Also, modal verbs in Afrikaans do not change form much for different persons:

• ek kan
• hy kan
• ons kan

So kan stays the same.

Because my is the possessive form used directly before a noun.

• my boek = my book

You use myne when the noun is not said and you mean mine:

• Die boek is myne. = The book is mine.

So:

• before a noun: my boek
• standing alone: myne

In this sentence, leen means borrow:

• hy my boek kan leen = he can borrow my book

Afrikaans can sometimes rely on context with leen, but if someone wants to make lend out especially clear, uitleen is also commonly used.

So for this sentence, the learner should understand leen as borrow.

Dit means it, and it refers back to my boek.

So instead of repeating die boek or my boek, Afrikaans uses the pronoun:

• maar hy belowe om dit vanaand terug te gee
• but he promises to give it back tonight

This works just like English:

• my book ... give it back

After belowe (promise), Afrikaans commonly uses an infinitive construction with om ... te.

So:

• hy belowe om dit ... te gee
• he promises to give it ...

Think of om ... te as the usual Afrikaans way of expressing to + verb in many structures.

Here:

• om introduces the infinitive phrase
• te gee = to give

Because teruggee is a separable verb.

Its basic meaning is:

• teruggee = give back / return

When Afrikaans uses te with this kind of verb, the particle and the verb split apart:

• terug te gee

That is normal.

Compare:

• Hy gee dit terug. = He gives it back.
• Hy belowe om dit terug te gee. = He promises to give it back.

So the split is caused by the te construction.

Vanaand means tonight / this evening.

It is a time word, and Afrikaans often places time expressions before the final infinitive part of the clause:

• om dit vanaand terug te gee

That placement sounds natural and clear. Afrikaans word order with adverbs is somewhat flexible, but this position is very common.

Yes, but dit is more natural because the book has already been mentioned.

Compare:

• ... maar hy belowe om dit vanaand terug te gee.
  Natural and smooth.

• ... maar hy belowe om my boek vanaand terug te gee.
  Also possible, but more repetitive.

So using dit is the normal way to avoid unnecessary repetition.