Learn Dutch: Denk je dat dat klopt? - Do you think that that is correct?

The first dat is the conjunction connecting the two parts of the sentence ("Do you think that..."). The second dat is a pronoun referring to a specific thing, like a statement or a math answer ("...that is correct?"). English does the exact same thing in "Do you think that that is correct?".

Why does the verb klopt go at the very end of the sentence?

The first dat (the conjunction) introduces a subordinate clause. In Dutch, these dependent clauses always push their working verb to the very end. Because of this rule, klopt gets pushed all the way to the back.

I thought the verb kloppen meant "to knock". How does it mean "is correct" here?

You are right that kloppen literally means "to knock" (on a door) or "to beat" (like a heart). However, in everyday Dutch, it is also used figuratively to mean "to add up", "to make sense", or "to be correct". You will hear the phrase Dat klopt! (That's right!) all the time.

Why is it Denk je without a -t at the end of the verb?

Because this is a question, the verb and subject swap places. In Dutch, whenever the subject je or jij comes directly after the verb, you must drop the -t ending. It is Je denkt (You think), but Denk je? (Do you think?).