The sentence that is punctuated correctly is the first one: My karate gi is made of heavy cotton fabric that pulls away moisture.
The word after karate (gi) should not be written between single nor double quotation marks. Quotation marks around a single word are added when the speaker wants to put emphasis on a word that someone else has used. Therefore, the second, third and fourth options are incorrect because they have added quotation marks around gi, which forms a noun together with karate. Karate gi is used to refer to the uniform that someone wears to practise karate.
Answer:
My karate gi is made of heavy cotton fabric that pulls away moisture.
Explanation:
