What are you going to do after school?
1. I am going to go to academy.
2. I am going to go to an academy.
3. I am going to go to the academy.
4. I am going to go to my academy.
5. I am going to go to private institute.
6. I am going to go to a private institute.
7. I am going to go to the private institute.
8. I am going to go to my private institute.
(Which answers are grammatical? Which answers are common ones?)
#3 is grammatically correct
#2 is commonly used
#6 is grammatically correct
#7 is commonly used
I'm almost positive
nautica is correct.
4 and 8 are also correct if the listener knows which academy is yours ... the one you attend.
All of the answers you provided are grammatically correct. However, the commonness of each phrase may vary depending on the context and individual preferences.
In general, phrases 1, 2, 3, and 4 are more commonly used when referring to an academy as a specific institution that you regularly attend or belong to. For example, if you are enrolled in a music academy, you might say, "I am going to go to the academy." The use of "the" implies that there is only one specific academy you are referring to.
Phrases 5, 6, 7, and 8, on the other hand, are more commonly used when referring to a private institute without specifying a particular one. For instance, if you are planning to join a private institute for extra tutoring, you might say, "I am going to go to a private institute." The use of "a" suggests that you are talking about one of many possible private institutes.
Ultimately, the preference for using "the" (phrases 1-4) or "a" (phrases 5-8) may depend on the specific academy or private institute you are referring to, as well as the level of specificity you want to convey in your statement.