Kun jij deze grafiek toelichten, of zal ik het doen?

Because this is a yes/no question in Dutch. In yes/no questions, the finite verb normally comes first.

• Statement: Jij kunt deze grafiek toelichten.
• Question: Kun jij deze grafiek toelichten?

The same thing happens in the second part:

• Statement: Ik zal het doen.
• Question-like offer: Zal ik het doen?

So Dutch often uses verb first where English uses do or changes intonation.

When jij/je comes after the verb because of inversion, the verb usually loses the -t ending.

So:

• jij kunt = statement order
• kun jij = inverted order

That is why kunt jij is not the normal standard form here.

With kunnen, learners also sometimes expect kan jij, because kan is another present-tense form of the verb. In standard Dutch, kun jij is the safest and most expected form in this sentence.

Because grafiek is a de-word.

In Dutch:

• deze is used with de-words
• dit is used with het-words

So:

• de grafiek → deze grafiek
• het boek → dit boek

A good habit is to learn the noun together with its article: de grafiek.

Because the sentence uses the modal verb kunnen. After a modal verb in Dutch, the main verb usually goes to the end of the clause in the infinitive.

So the structure is:

• Kun = finite modal verb
• jij = subject
• deze grafiek = object
• toelichten = main verb at the end

This is very common in Dutch:

• Ik kan komen
• Zij wil helpen
• Kun jij deze grafiek toelichten?

Here toelichten means something like explain, clarify, or comment on in a helpful way.

With something like een grafiek, een tabel, or een plan, toelichten often sounds a bit more formal or professional than uitleggen.

So:

• uitleggen = explain in a broad, general sense
• toelichten = explain/clarify, often by giving extra detail or commentary

In a meeting or presentation, deze grafiek toelichten is very natural Dutch.

Yes. Toelichten is a separable verb.

That means:

• as an infinitive: toelichten
• in a main clause with a finite verb: Ik licht deze grafiek toe.

So in your sentence, it stays together because it is an infinitive after kun:

• Kun jij deze grafiek toelichten?

But in a normal statement without a modal:

• Jij licht deze grafiek toe.

This is a very common Dutch pattern with separable verbs.

Because Dutch, like English, often avoids repeating the whole verb phrase when it is already clear from context.

Here het doen means do it, and het stands for the action of deze grafiek toelichten.

So:

• Kun jij deze grafiek toelichten, of zal ik deze grafiek toelichten?
• more natural: Kun jij deze grafiek toelichten, of zal ik het doen?

This is completely normal and sounds more natural than repeating the full phrase.

Het refers to the whole action mentioned before: deze grafiek toelichten.

So het doen means:

• do that
• do it
• specifically here: explain the graph

Dutch often uses het as a neutral placeholder for an action, situation, or previously mentioned idea.

Not exactly. Here zal ik is not mainly about the future. It is an offer or suggestion, similar to English shall I...?

So:

• Zal ik het doen? = Shall I do it?

This use of zullen is very common for polite suggestions or offers:

• Zal ik helpen?
• Zullen we beginnen?

So in this sentence, the speaker is offering to explain the graph if the other person does not want to.

Both are possible:

• Kun jij deze grafiek toelichten?
• Kun je deze grafiek toelichten?

The version with jij often feels a bit more emphatic or focused on the person.

It can suggest something like:

• Can you explain this graph?
• as opposed to someone else doing it

The version with je is a little more neutral and less emphatic. In real speech, the difference can be small, but jij often adds extra focus.

Of here means or.

It connects two alternatives:

• Kun jij deze grafiek toelichten
• of zal ik het doen

So the speaker is offering a choice:

• either you explain the graph
• or I will do it

This is a very common use of of in Dutch.