There are three very different uses of that : Subordinating that : “I know that this is the answer.”
Demonstrative pronoun that : “ That is not the answer.”
Adjectival
that : “ That answer is not it.”
Double that occurs because the first that is the subordinating that , and the second that is a demonstrative pronoun or adjectival that .
That is, if you subordinate a clause that begins with pronominal or adjectival that with that , you get that that , as in “you know that that that that from the previous sentence was different from the one in this sentence.”
english.stackexchange.com/users/39/nohat
Of course it is acceptable grammar .
The rules of English grammar are the very reason why such "strange things" happen in the first place.
Now, whether or not you actually end up using a double "that" or rewording it, is a different question.
But it is a question of style .
Read: personal preference.
Personally, more often than not, I don't find a double "that" to be distracting or leading to confusion at all.
Quite the contrary: it is a) perfectly self-explanatory and b)
it certainly leads to less confusion than leaving one of those "that"s out.
english.stackexchange.com/users/300/RegDwigнt
I don't think that that is a problem.
Having said that, it would still make sense if one of the "that"s in the previous sentence were omitted.
EDIT:
In response to Reg's comment: If a "that" is omitted, it's the first one that is removed.
Replacing the second "that" with "it" may clarify things: I don't think that it is a problem.
I don't think
it is a problem.
Hence saying "I don't think that is a problem" is fine - as long as you're familiar with this particular usage of the word "that".
If not, then it could obviously cause confusion.
english.stackexchange.com/users/303/Steve Melnikoff
This is correct.
The two words are performing different functions.
The first that is used to introduce a clause.
The second that is used to refer to a specific thing.
english.stackexchange.com/users/6434/Yozomiri
I would argue that it might very well be correct, but if it makes you uncomfortable, it may also distract your readers.
You've likely seen the common example: The human brain often skips any extra words that appear in the the sentence they're reading The same behaviour might happen with the extra "that" appearing in your sentence.
So while it might be correct in theory, perhaps you could reword your sentence such that it becomes more readable for your audience.
english.stackexchange.com/users/4136/Phil.Wheeler
It's perfectly fine to write "that that" or to simply write "that": your choice, your style, your need at the moment.
english.stackexchange.com/users/2303/Robusto
If the question is about how do I handle the problem personally, I always try to minimize my usage of the word "that" in order to avoid these instances altogether.
"
That bike that is blue" becomes " the bike which is blue" or simply, "the blue bike."
Therefore: "That that is blue" becomes "that which is blue" or even "what is blue" in some contexts.
"I know that it is true" becomes "I know it is true."
I simply omit the word "that" and it still works.
"That that is true" becomes "That which is true" or simply, "The truth."
I do this
not because it is grammatically incorrect, but because it is more aesthetically pleasing.
The overuse of the word "that" is a hallmark of lazy speech.
Indeed, if avoiding these instances causes you to think outside the box, your speech and writing will become more fresh and creative as a result.
To clarify, I don't go out of my way to avoid the word "that."
I simply reduce my daily usage of it in order to avoid confusion.
english.stackexchange.com/users/108585/Adrian W
I use 'that that' quite often because it gives you an explicit reference to the exact subject referred to previously.
Simply replacing it with 'this' sometimes will not do as I sometimes wish to refer to 'that' specifically.
english.stackexchange.com/users/78106/WarmMilkYo
Have you ever had a case where you felt compelled to include strange things like a double  that  in a sentence? If so, then what did you do to resolve this?  For me, I never knew whether it was acceptable grammar. However, what I did learn was that it was a  logic distractor , could lead to confusion, and therefore should be reworded to avoid this.
How do you handle "that that"? The double "that" problem
english.stackexchange.com
<adjectives><pronouns><sentence-patterns><repetition><doubled-words>
english.stackexchange.com/questions/3418
english.stackexchange.com/users/1416/Volomike
In is generally agreed that "that that" is not a problem in English grammar. However, you might want to re-word a sentence such that it becomes more readable for your audience. It is correct because both words are performing different functions. The first "that" is introducing the subordinate clause and the second one is a demonstrative adjective.  However, for stylistically the word choice could be changed so as not to confuse the reader. It is not distracting, so it is perfectly fine to use both "thats" in this sentence. Indeed, the human brain has a tendency to skip words, so in this sentence, this could be of benefit here where the second "that" is ignored.
In is generally agreed that "that that" is not a problem in English grammar. However, you might want to re-word a sentence such that it becomes more readable for your audience. This is acceptable  grammar and is a question of  style . It would still make sense if one of the "that"s in the sentence were omitted.  Replacing the second "that" with "it" may clarify things:   I don't think that  it  is a problem.  But bear in mind that the two words are performing different functions.
A double "that" is not distracting and does not lead to confusion. However,  you may prefer to reword your sentence so that it becomes more readable for your audience. In is generally agreed that "that that" is not a problem in English grammar. However, you might want to re-word a sentence to remove "that that" if you feel it will make a more comfortable read.
It is correct because the first "that" is introducing the subordinate clause and the second one is a demonstrative adjective.  Both words are performing different functions. For clarification, the word choice could be changed.
This is acceptable  grammar and is a question of  style . It would still make sense if one of the "that"s in the sentence were omitted.   Replacing the second "that" with "it" may clarify things:   I don't think that  it  is a problem.   But bear in mind that the two words are performing different functions.
It is generally agreed that this is not a grammar problem in writing. You may want to re-word your sentence in order to remove instances of "that that" if you feel that it will make a more comfortable read.