Ik denk dat dit antwoord klopt.

Because dat introduces a subordinate clause: dat dit antwoord klopt.

In Dutch, subordinate clauses usually send the conjugated verb to the end.

• Main clause: Dit antwoord klopt.
• Subordinate clause: ... dat dit antwoord klopt.

So Ik denk is the main clause, and dat dit antwoord klopt is the clause being thought.

Here, dat means that and works as a conjunction.

It links the two parts of the sentence:

• Ik denk = I think
• dat dit antwoord klopt = that this answer is correct

This dat is different from demonstrative dat meaning that as in that book.

Because antwoord is a het-word: het antwoord.

For singular nouns, Dutch uses:

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

So:

• deze vraag because de vraag
• dit antwoord because het antwoord

Because dit already functions as a demonstrative determiner.

In Dutch, you normally do not combine an article and a demonstrative before the same noun.

So you say:

• dit antwoord
• not dit het antwoord

It works like English this answer, not this the answer.

Here kloppen means to be correct, to be right, or to be accurate.

It has other meanings too, depending on context, such as:

• to knock
• to beat or to throb
• to match up

But in dit antwoord klopt, it clearly means this answer is correct.

Kloppen is the infinitive, meaning to be correct or to knock.

In the sentence, the verb is conjugated for the singular subject dit antwoord, so you get klopt.

Present tense forms:

• ik klop
• jij klopt
• hij/zij/het klopt

Since dit antwoord is singular, klopt is the correct form.

Yes, in informal Dutch, you often can.

So you may hear:

• Ik denk dat dit antwoord klopt.
• Ik denk dit antwoord klopt.

When dat is left out, the second part often keeps main-clause word order, so klopt stays after the subject.

For learners, though, it is safest to keep dat, because that version is fully standard and very common.

Yes. Dit antwoord klopt, denk ik is also natural Dutch.

The meaning is very similar, but the focus shifts slightly:

• Ik denk dat dit antwoord klopt starts with I think
• Dit antwoord klopt, denk ik starts with this answer is correct

So the second version foregrounds the answer, while the first foregrounds your opinion.

Both are common and correct.