What does "grammatically correct" mean?
Hi and welcome to the forum.
"Grammatically correct" means that something (writing or speaking) follows the rules of grammar.
He go to the store (incorrect grammar)
He goes to the store (grammatically correct)
Despite what many people think, the "rules" of grammar are an attempt to describe (in a logical/consistent) fashion how people use language. They grow out of the (obvious) observation that all languages show consistent patterns of usage. To say that something is ungrammatical means nothing more than that this is not a commonly used pattern (or, more precisely, the construction is so unusual as to render it hard-to-understand.
Even the, so-called, "prescriptive" grammarians are only stating with their "You should say it this way." This is the way I would say it (a descriptive statement) and, therefor, you should say it the same way (a prescriptive statement but one of questionable value).
Languages (any language) are not a collection of random utterances. There exist consistent patterns (and exceptions [but the patterns dominate]).
The dividing line comes when you have patterns that are different from the traditional ones but are, nonetheless, widely used. If their use is sufficiently widespread, they become established but as "exceptions" to the usual patterns (no doubt after protestations from the prescriptive grammarians).
The phrase means using correct grammar. SOunds like homework to me but the rest of your request is unclear.