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Most of the time, if you see "that" after a noun, then you're looking at a noun modifier (and the "that" modifier is modifying the noun before it, though it may also be modifying not that noun but the main noun before it - eg, The box of nails that I opened. I opened the box, not the nails.).
The "that" modifier is actually using the word "that" as a relative pronoun.
Then, separately, "that" can also be used as a necessary extension in a core sentence. Most of the time, the word "that" (in this case) will follow a verb.
She believes THAT studying is important.
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Stacey Koprince
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Manhattan GMAT
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