Denk je dat jij erin zult slagen om dit verslag vanavond af te maken?

Because this is a direct yes/no question.

In Dutch, a main-clause yes/no question normally puts the finite verb first:

• Je denkt dat ... = statement
• Denk je dat ...? = question

So Denk je dat ...? is the normal Dutch equivalent of Do you think that ...?

Yes, both mean you, but they are used differently:

• je = unstressed, neutral form
• jij = stressed, emphatic form

So:

• Denk je dat je erin zult slagen ...? = neutral
• Denk je dat jij erin zult slagen ...? = emphasizes you

In this sentence, jij can suggest something like:

• Do you think that you, specifically, will manage ...?
• contrast with someone else
• a bit more emphasis or challenge

The first je after Denk is the normal weak form used in everyday speech.

Erin slagen is a fixed expression meaning to succeed in, to manage to.

So:

• ergens in slagen = to succeed in something
• erin slagen om iets te doen = to succeed in doing something

Here, erin does not translate neatly as a separate English word. It points to the action that follows:

• erin zult slagen om dit verslag ... af te maken

So the whole idea is:

• to succeed in finishing this report tonight
• or more naturally in English, to manage to finish this report tonight

This kind of er + preposition combination is very common in Dutch.

Because dat introduces a subordinate clause.

In Dutch subordinate clauses, the finite verb usually moves toward the end of the clause area.

Compare:

• main clause: Jij zult erin slagen
• subordinate clause: dat jij erin zult slagen

So after dat, Dutch normally puts:

1. subject
2. other elements such as adverbs or pronoun-adverbs
3. the verb group later

That is why you get:

• dat jij erin zult slagen

and not the main-clause order:

• dat zult jij erin slagen ← incorrect

Zult is a form of zullen.

Here it is the 2nd person singular form used with jij/je:

• ik zal
• jij zult
• hij zal
• wij zullen

In this sentence, zult helps express the future:

• jij zult slagen = you will succeed / you will manage

So zult slagen is roughly will succeed or will manage.

In everyday spoken Dutch, people sometimes use zal with je/jij, but zult is the standard form learners should know.

Because om ... te + infinitive is a common way to introduce an infinitive clause, similar to English to + verb.

Here the infinitive clause is:

• om dit verslag vanavond af te maken

It depends on slagen:

• erin slagen om iets te doen = to manage to do something

So the structure is:

• Denk je dat jij erin zult slagen
  om dit verslag vanavond af te maken?

In English, we would usually just say to finish. Dutch often uses om ... te in this kind of structure.

Because afmaken is a separable verb.

The full verb is:

• afmaken = to finish, to complete

When a separable verb appears with te, the prefix and the verb split:

• afmaken
• af te maken

This is very common in Dutch:

• opschrijven → op te schrijven
• uitleggen → uit te leggen
• afmaken → af te maken

So af te maken is exactly what you should expect.

Maken means to make or to do.

Afmaken means to finish, to complete, or to make something all the way to the end.

So:

• een verslag maken = to write/create a report
• een verslag afmaken = to finish the report

In this sentence, the report already exists or is underway, and the question is whether the person can finish it tonight.

Vanavond is a time adverb meaning tonight. In Dutch, time expressions often appear in the middle of the clause, before the final verb part.

Here it sits inside the infinitive clause:

• om dit verslag vanavond af te maken

This is a very natural position.

You may also see other word orders depending on emphasis, but this one is standard and smooth. The sentence is focusing on the action finishing the report tonight, so vanavond comes right before af te maken.

It is grammatical and natural, but it sounds a bit more formal or careful than everyday casual speech.

Very common everyday alternatives would be:

• Denk je dat het je lukt om dit verslag vanavond af te maken?
• Denk je dat je dit verslag vanavond af krijgt?

These are often more conversational.

The original sentence with erin zult slagen is perfectly good Dutch, but it sounds a bit more like Do you think you will succeed/manage to ...?, which is slightly more explicit or formal.

Yes.

• Denk je dat je erin zult slagen ...? = neutral, everyday
• Denk je dat jij erin zult slagen ...? = more emphasis on you

So the version with jij is not wrong at all, but it adds stress. If there is no special contrast or emphasis, many speakers would simply say dat je.