You probably want to declare your method like this:
+ (NSMutableString *)userVisibleDateTimeStringForRFC3339DateTimeString:(NSMutableString *)rfc3339DateTimeString formatString:(NSString *)rfc3339DateTimeFormatString;
(Note the + at the start, and the fact that the second argument is now named - it was blank in your code, which is valid but weird.)
Then you'd call it like this:
predicateMutableString = [jhsDateFormatter userVisibleDateTimeStringForRFC3339DateTimeString:dateHolderMutableString formatString:@"yyyy'-'MM'-'dd'"];
Where jhsDateFormatter the new class you've made.
In your example code, you're not calling the method on any object, which is why the compiler is complaining.