Which sentence is punctuated correctly? my karate gi is made of heavy cotton fabric that pulls away moisture. my karate “gi” is made of heavy cotton fabric that pulls away moisture. my karate “gi” is made of heavy cotton fabric that pulls away moisture. my karate ‘gi’ is made of heavy cotton fabric that pulls away moisture.

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.  

and your question what topic are you in trouble with?